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\title{Macroscopic Spacetime Shortcuts in the Manyfold Universe and the Abnormal Gravitomagnetic Fields in Rotating Superconductors}
\author{Fernando Ernesto Gorjao Henriques de Carvalho e Rego Loup \footnote{spacetimeshortcut@yahoo.com}\\
Faculdades Integradas Anglo Americano - Botafogo -  Rio de Janeiro
- Brazil(851101667 - 1985)}

\maketitle

\begin{abstract}
Recently the idea of a Manyfold Universe was proposed by some
authors to explain Dark Matter . In this study we assume that the
Standard Model(SM) of particles and fields with gravity
propagating in the Higher Dimensional Spacetime(Bulk) while other
interactions are confined to 3+1 Einsteinian spacetime(Brane) is
not due to open strings and closed loops but instead is due to the
capability of gravity as the weakest and "smallest" interaction to
penetrate these small Bulk size ($10^{-31}$m to $10^{-35}$m) while
protons,neutrons and other interactions stronger and "larger" than
gravity do not "fits" in the size of the Bulk and remains trapped
on the Brane and we present a equation to justify this point of
view. Our picture relies over the geometrical beauty of the
Manyfold Universe proposal that Dark Matter is chemically
identical to ordinary matter but lies on other Folds. We present
the fact that the exotic particles such as
Photinos,Axions,WIMPS,Neutralinos etc all created to explain the
Mistery of Dark Matter dont have physical existance because these
were not found by a precise instrument as the NASA Chandra
Satellite and NASA agrees with the Manyfold Universe and we will
shall see this in the text. Also the geometrical point of view for
the small size of the Bulk eliminates the need of trapping
mechanisms to confine matter in the Brane based on exotic physics
(eq Quintessence Fields or Einstein Cosmological Constant)
providing a geometric trapping mechanism of natural beauty. Matter
cannot enter the Bulk because its size is "larger" than the size
of the Bulk itself. Also we "enlarge" the "size" of the Bulk from
$10^{-35}$m to $10^2$m demonstrating that the Newtonian Gravity
Constant in 3+1 Dimensions $G_4$ remains constant and the
Newtonian Gravity constant $G_5$ is the affected by this "Bulk
Enlargement" so in our model large dimensions are not tied up or
constrained by the $\frac{1}{d^2}$ to $\frac{1}{d^3}$ that in
large Newtonian spaces could affect for example planets orbits and
we compute the energy density of this process and although we
still dont know a physical process to enlarge the size of the Bulk
(and we have only a theoretical mathematical model as a
"fingerprint" but perhaps rotating superconductors can provide the
desired answer and we show how a rotating superconductor can
"enlarge" the Extra Dimension from Planck Size to Macroscopical
one) the energy density remains low and physically affordable.
Perhaps if this process will be discovered someday using rotating
superconductors it will be able to explore the Bulk "Superluminal"
properties and produce a Macroscopic Spacetime Shortcut in the
Manyfold Universe that would allow the "Hyperfast" communication
between distant regions of the Universe that otherwise would be
far away distant forever.

\end{abstract}

%%%%%%
\section{The Manyfold Universe(ADDK)-Nimas Arkani Hamed,Savas Dimopolous,Gia Dvali,Nemanja Kaloper}
\indent\indent Recently Nimas Arkani Hamed(A),Savas
Dimopolous(D),Gia Dvali(D) and Nemanja Kaloper(K) proposed the
Manyfold Universe to explain Dark Matter \cite{ref1}. In this
model our Universe is folded or bended over itself and distant
parts at billion light years of distance from each other in the
Brane are really at milimeters of distance in the Bulk (pp 988
figure of the Japanese Origami in \cite{ref2}) and (pp 4 fig 1 in
\cite{ref1}). We adopt the fact that these "entrances" to the Bulk
are so small of the order of $10^{-35}m$(pp 3 in \cite{ref5} and
pp 7 in \cite{ref3}) that only gravity as the weakest and
"smallest" interaction \cite{ref2} can afford to enter in the
Bulk. This framework is somewhat different than the usual one of
open strings and closed loops (pp 987 in \cite{ref2})( pp 4 fig 2
in \cite{ref5} and pp 25 fig 11 \cite{ref5}) because it is the
size of the Bulk too small enough to be penetrated by protons
neutrons and other SM interactions that acts like a geometric
trapping mechanism of natural beauty that under the SM conditions
allows gravity to slip into the Bulk retaining in the Brane all
the rest of SM fields and matter(pp 3 in \cite{ref5} and pp 7 in
\cite{ref3}) without the need of exotic physics(Quintessence
Fields or Einstein Cosmological Constant (pp 2,3 and 5 in
\cite{ref3}).We also use a equation to give mathematical
consistence for this point of view(pp 12 eq 14 in \cite{ref5}).
According to ADDK model gravity can use the Bulk Shortcuts to
travel billion light years in matter of seconds in the Bulk(pp
987,988 in \cite{ref2}) and (pp 3,16 in \cite{ref1}) while light
needs large amounts of time to cover the same distance in the
Brane. Then the gravity of a newly formed star at billion light
years would arrive to us in minutes but the object would appear to
us as Dark Star until the arrival of the first photons of light(pp
4,5 in \cite{ref1}). Consider for example a star formed in a
Galaxy at 326 million light years away:the gravity of the formed
star will reach us in $2,5*10^{-10}$ seconds travelling in the
Extra Dimension of Planck size while photons of light confined to
our 3+1 space needs 326 million light years to cover the same
distance (pp 8 in \cite{ref3}). Now we have a clear picture of
what "Dark Matter" really is:our star newly formed at 326 million
light years away will interact gravitationally with matter in our
local neighbourhoods in $2,5*10^{-10}$ seconds after the star
formation creating a ADDK Hybrid Object but during the first 326
million years of existance the star will remain to us a "Dark"
star until the arrival of the first photons of light to make the
star "shine" and "visible".( see pp 5,6 in \cite{ref1} about the
comment that a observer can "see" the "Dark Matter" if the
observer waits long enough). When we measure the gravitational
field of a body we measure the gravitational field of more than
one component at perhaps billion light years of distance from each
other although connected by a submilimeter extra dimension and
this combination is called by the Manyfold Universe creators(ADDK)
as a "Hybrid Object" (pp2 in \cite{ref1}).If we measure the
gravitational part of the visible component of course we will find
that this is less than the whole field.The difference is the
so-called "Dark Matter". The attempts of Axions,WIMPS,Neutralinos
and all the SUSY Particles are not able to solve this problem
\cite{ref11} and NASA agrees with the Manyfold Universe(ADDK)
Model \cite{ref11}


The "Superluminal" properties of the Extra Dimension were already
noticed by ADDK authors (see pp,3,16 in \cite{ref1} and pp 8 in
\cite{ref3}). This does not means to say that gravity propagates
at "Superluminal" speeds:it means to say that gravity can take the
shortcuts thru the Extra Dimension that connects at Planck size
remote parts of the Universe at billion light years away arriving
first than photons of light to these remote parts since photons
are confined to our ordinary spacetime and cannot take shortcuts.
If we assume that there exists a physical process to enlarge the
size of the Bulk from $10^{-35}m$ to $10^2m$ and although this
process remains unknown (and we have only a theoretical
mathematical model but rotating superconductors can provide the
right answer and we will demonstrate this in the text body of this
work)( pp 12 eq 14 in \cite{ref5}) we compute the energy density
and surprisingly we demonstrate that this enlargement needs low
and affordable energies.Dark Matter is the strongest proof that we
live in a Hyper Dimensional Universe\cite{ref1,ref4}.Astronomers
are detecting Dark Matter even in our galaxy not at billion
light-years away \cite{ref4} (pp 5 in \cite{ref1})where our
instruments can give measures with precision.It is difficult to
spot a source at billion light years away but a source at 100.000
light years away is well within our capability.This is a fact not
a exotic theory and this matter do not have a “physical component
as a body”. The gravity of distant objects at billion light years
away in the ordinary 3+1 spacetime are really at milimeters of
distance in a Hyper Dimensional Universe and gravity can take the
shortcut to reach us in minutes while light needs to travel
billion light years(pp 2 in \cite{ref1}). All we have to do is to
enlarge these tiny spacetime shortcuts from $10^{-31}$ meters to
$10^2$ meters large enough to contain macroscopic
bodies(\cite{ref6})…and then we will be able to explore distant
parts of the Universe.( pp 12 eq 14 in \cite{ref5}) We need to
enlarge these tiny holes from $10^{-31}$ meters(considering a Bulk
of this size) to $10^2$ meters keeping the $G^{00}$ of the
Einstein Field Equations the energy density low and close to
zero(assuming that we need some form of energy to "enlarge" the
Bulk then we must worry ourselves about the amount of energy
needed) because we will increase a dimension from $10^{-35}$
meters to $10^2$ meters.We will raise a volume by a magnitude of
$10^{37}$ roughly speaking we will multiply by
10.000.000.000.000.000.000.000.000.000.000.000.000 times and if
$G^{00}$ is between 0 and 1 but in the neighbourhoods of 1 this
process will require a unphysical amount of energy.We must keep
our $G^{00}$ between 0 and 1 but close to zero to keep the energy
at a physical reasonable level and we need also to discover a real
physical process to enlarge these tiny holes.Rotating
Superconductors seems to be the right path .Then if we can figure
out this process we can perhaps open a Macroscopic Spacetime
Shortcut in the Manyfold Universe connecting remote regions of the
Universe(\cite{ref6}) that otherwise would be far away distant
forever.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Bulk Topology - The Japanese Origami}
\indent\indent In the Japanese Origami (pp 988 in \cite{ref2}) and
(pp 4 fig 1 in \cite{ref1} and "Manyfold Universe" picture in
\cite{ref4}) we can see a folded 3+1 region of Einstein Universe
with a lenght of billion light years and with two BraneFolds(one
left and another right) separated by a milimeter distance in the
Bulk.In order to trap SM fields in each Brane allowing only
gravity to slip from one Brane to another the “throat” can have
milimeters in lenght but must have a restraint of about
$10^{-35}m$ width and height acting as a "bottleneck" trapping
protons and neutrons larger than the “throat” in the Brane while
gravity travels in the Bulk.This "throat" is the "SM bottleneck"
and in the next section we will present the equation of this
"bottleneck".

Another idea for this "throat" can be figured out looking also to
the picture in (pp 3 in \cite{ref5}).The straight line can be the
"milimeter" distance between two Branefolds in the ADDK model but
the straight line is actually a cylinder of radius $10^{-35}$ m.

The Bulk dimension $R$ is composed by $R^2=p^2 + q^2 + r^2$ where
$p$ is the milimeter distance and q and r are the $10^{-35}$m
"throat bottleneck".

Initially $R^2=2*10^{-35}$ and $p=0$ (Left Brane) or $p=10^{-3}$m
(Right Brane) and $R$ corresponds to the Bulk in \cite{ref3}. Note
that $10^{-35}$m is so small that $R$ is close to zero and the
ansatz of \cite{ref3} reduces to a SR ansatz(Reductions to SR
ansatz will be further mentioned in this work).

If we want a throat with $10^2$m wide then $q,r=10^2$ and $R^2 =
p^2 + 2*10^2$.Negleting $p$ for $0$ and $10^{-3}$ (or $10^{-6}$
for $p^2$) then $R^2=2*10^2$ and $R=\sqrt(2)*10$. This resembles
the $R=15$ from (pp8 in \cite{ref3}) .

But what if we could discover a way to "enlarge" this Planck size
dimension from $10^{-35}$ m to 200 meters The Planck size of the
Extra Dimension can be written in function of some well-known
physical constants and the expression was obtained by a research
group in the University of Amsterdam Holland(pp 12 eq 14 in
\cite{ref5}).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Enlarging The Bulk Dimension from The Planck Length To A Macroscopical Size  - The Dutch Equation-Szczepan W.
Kowalczyk,Jorn Mossel} \indent\indent

Recently some researchers in Holland (Kowalczyk,Mossel et
al)(\cite{ref12,ref13}) studied the behaviour of gravitation in
$5$ dimensions considering all the well-known and proved
experimental physics and they arrived at a very interesting
result. A equation giving the radius of the extra dimension as the
Planck Length in function of some physical constants.( pp 12 eq 14
in \cite{ref5}). This equation is fundamental in our study to
"enlarge" the Bulk to a Macroscopical size and will be further
mentioned as the Dutch Equation.By changing the values of some
physical constants we will "enlarge" the size of the Bulk.Also
Marc Millis from NASA conjectured the possibility to alter some
physical constants to create space propulsion(altering the value
of the gravitational constant $G$ Bias Drive in \cite{ref6}).We
prefer to do not change the value of $G$ and instead we choose to
manipulate the values of electric and magnetic permeability and
permissivity in the vacuum to "change" the size of the Bulk to
Macroscopical.

The Dutch Equation is:

\begin{equation}  \label{eq1}
R = \sqrt\frac{4\pi\epsilon_0G\hbar^2}{\epsilon^2c^2}
\end{equation}

This equation shows the relation between some physical constants
and the geometry of a spacetime.By changing the constants we will
change the geometrical properties of the Bulk and the behaviour of
a given spacetime can be "engineered"\cite{ref6}.This is why the
Dutch Equation is so important:the beauty of spacetime geometry
related to physical constants.In the Dutch Equation $R$ is the
radius of the Bulk,$\epsilon$ is the elementary charge of the
electron,$\hbar$ is the Planck Constant,$G$ is the Newton
Gravitational Constant and $\epsilon_0$ is the electric
permeability of the vacuum.Inserting the known values of the
constants we will get a result $R=1.9*10^{-34}$m near the Planck
Length.Note also that the size of the Bulk dimension depends only
on constants of our physical dimension and this is very good for a
spacetime "manipulation"\cite{ref6},otherwise we would never be
able to "control" the Bulk geometry.This another important point
of the Dutch Equation.

We choose to work with the electric permeability of the vacuum
because eletromagnetic interactions are a well understood
phenomema and more easily controllable\cite{ref6}.

Enlarging the electric permittivity in the vacuum by a still
unknown physical process we will "uncurl" the extra dimension
allowing Macroscopic Shortcuts.We hope that Rotating
Superconductors can provide the final answer.

By enlarging $\epsilon_0$ to $\epsilon_1$ a we will raise the size
of the Bulk dimension to Macroscopical one but we want to keep
$c=\frac{1}{\sqrt(u_0\epsilon_1)}$ constant to do not break the
Lorentz invariance and retains the laws of electromagnetism valid
as many as possible.Then our physical process that will raise the
$\epsilon_1$ will proportionally low the $u_0$ .

Working with $c=1$ implies that $\sqrt(u_0\epsilon_1)=1$ and we
can rewrite the Dutch Equation as:

\begin{equation}  \label{eq2}
R = \sqrt\frac{4\pi\epsilon_1G\hbar^2}{\epsilon^2}
\end{equation}

$R$ is directly proportional to $\sqrt\epsilon_1$ then we can
write $R=P_1\sqrt\epsilon_1$ where $P_1$ encompasses all the other
invariant constants.

In the next section we will also work with variables $\epsilon_0$
and $u_0$ because $c$ can also decrease(VSL Cosmology and Rotating
Superconductors).


We must consider that changing the $\epsilon_1$ we are changing
the behaviour of electromagnetism and perhaps affecting the
molecular or atomic structure of a macroscopic body:Then if we
want to enlarge the Bulk to allow the passage of the macroscopic
body to the higher dimensional spacetime we must create a
"geometric manipulation of spacetime"\cite{ref6} that will alter
$\epsilon_1$ in the neighbourhoods of the body but far away from
it and in the spacetime region where the body resides $\epsilon_1$
must remains unchanged.Our idea is to involve the body inside a
"bubble distortion" that will change $\epsilon_1$ in the "bubble
walls" enlarging the Bulk but inside the "bubble" and far away
from it the $\epsilon_1$ remains unchanged to preserve
compatibility with the known physical laws($\epsilon_1$ =
$\epsilon_0$).Perhaps Rotating Superconductors can open the
possibility to generate this process.

Enlarging $\epsilon_1$ we will decrease the Coulomb Constant
affecting the electric forces and the macroscopic body must remain
inside the "bubble" where $\epsilon_1= \epsilon_0$ to retain
intact its atomic structure.This must deserves further
investigation in the future because we reckognize that the Bulk
can be enlarged but inserting a "bubble" containing a Macroscopic
Body is somewhat still complicated.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The Variable Light Speed(VSL) Cosmology - Joao Magueijo }
\indent\indent

All our discussion of changing the electric permeability in vacuum
to create a shortcut to higher dimensional space would be regarded
as useless without a clue of realistic physical experimental
evidence that this is really possible. We choosed to change
electric permeability instead of $G$(Millis Bias Drive\cite{ref6})
because electromagnetism is a more well understood physical
interaction than gravity in agreement with Millis.\cite{ref6}. If
we change for example electric permeability in vacuum we may
change the value of the speed of light in vacuum and this would
not be a absolute constant.If light speed is or is not a constant
in the vacuum is one of the most controversial paradigms of modern
physics.This paradigm leads us to Joao Magueijo.(pp 5 in
\cite{ref7}).

Magueijo supports the argument that light speed is now slower than
it was billion of years ago.Although Magueijo is not alone
following this line of reason and he was not the first to propose
this idea,he is one of the most stronger and active supporters of
this idea.Experimental data obtained from supernova explosions
seems to confirm Magueijo point of view.(pp 38 in \cite{ref7}).

A variable light speed cosmology is very important to our point of
view of changing fundamental physical constants to enlarge Bulk
Size allowing Macroscopical Shortcuts:It provides the proof that
it really can be done,otherwise for a absolute and constant speed
of light our discussion would be completely useless.

If light speed varies with time then
$c=\frac{1}{\sqrt(u_0\epsilon_1)}$ depends on a variable
$\sqrt(u_0\epsilon_1)$ .Here we face the following scenarios:

\begin {itemize}
\item[1)] $u_0$ varies and $\epsilon_1$ is constant;

\item[2)] $u_0$ is constant and $\epsilon_1$ varies;

\item[3)] $u_0$ varies and $\epsilon_1$ varies.

\end {itemize}

In all the above cases the Dutch Equation will be affected and
since light speed slows down then the radius R of the Bulk
increases.The desirable situation for our case would be the second
item:a variation of electric permeability will affect the Dutch
Equation in upper and lower parts of the fraction while first item
affects only the lower part.The radius of the Bulk increases
because $u_0$ or $\epsilon_1$ increases.

Although this variation depending on time is pretty small and
needs billion years to be verified it really happens,opening the
hope that if it can happen in time perhaps the spacetime can be
"engineered" to produce a local variation on $u_0$ or $\epsilon_1$
depending on geometry and electromagnetism.(Millis in
\cite{ref6}).Perhaps a "vacuum polarization" as referred by
Magueijo in (abstract of \cite{ref7}) can be "engineered".

The desirable situation would be the one of eq 3 of previous
section.

We considered in the previous section a changing $\epsilon_1$ with
the corresponding changing in $u_0$ to make $c=1$.

If we consider a varying $c$ due to a increasing $\epsilon_1$
keeping $u_0$ constant,but having a variable $c$ then we must
rewrite the Dutch Equation as follows:

\begin{equation}  \label{eq4}
R = \sqrt\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2}
\end{equation}

Note that now $\epsilon_1^2$ have a more strong influence over the
Bulk Radius.

The relation between the size of the Bulk $R$ and $\epsilon_1$
would be given by :

\begin{enumerate}

\item $u_0$ varies and $\epsilon_1$ varies (fixed value $c=1$ the
case of previous section),$R=P_1\sqrt\epsilon_1$
,$R^2=P_1^2\epsilon_1$ ;

\item $u_0$ is constant and $\epsilon_1$ varies (variable
$c$),$R=P_2\epsilon_1$,$R^2=P_2^2\epsilon_1^2$ .

\end{enumerate}

Again as stated before for $P_1$,$P_2$ are the other constants in
the Dutch Equation.

The differentials of Bulk radius needed for the ansatz are given
by:

\begin {itemize}

\item[1)] $dR=P_2d\epsilon_1$ ;

\item[2)] $dR=\frac{1}{2}\frac{P_1}{\sqrt\epsilon_1}d\epsilon_1$ .

\end {itemize}

\begin {itemize}

\item[1)] $dR^2=P_2^2d\epsilon_1^2$ ;

\item[2)] $dR^2=\frac{1}{4}\frac{P_1^2}{\epsilon_1}d\epsilon_1^2$
.

\end {itemize}

This allows us to write the General Relativity ansatz in function
of the variation of the electric permeability in vacuum.

Note that the values of $P_1=\frac{2}{\epsilon}\hbar\sqrt(\pi G)$
and $P_2=2\frac{\hbar}{\epsilon}\sqrt(\pi Gu_0)$ are low of the
order $0 < G < 1$ and $0 < \hbar < 1$ because of the values of
$G=6,67*10^{-11} Nm^2/Kg^2$ and $\hbar=\frac{6,626}{2\pi}*10^{-34}
Js$ that divided by $\epsilon=1,6*10^{-19} C$ will still produce
low values although $P_2 < P_1$ due to $u_0 = 4\pi * 10^{-7} H/m$.

Then $0 < P_1 < 1$ and $0 < P_2 < 1$ and

\begin {itemize}

\item[1)] $\frac{dR}{d\epsilon_1}=P_2$ ;

\item[2)]
$\frac{dR}{d\epsilon_1}=\frac{1}{2}\frac{P_1}{\sqrt\epsilon_1}$ .

\end {itemize}

\begin {itemize}

\item[1)] $(\frac{dR}{d\epsilon_1})^2=P_2^2$ ;

\item[2)]
$(\frac{dR}{d\epsilon_1})^2=\frac{1}{4}\frac{P_1^2}{\epsilon_1}$ .

\end {itemize}


Note that the derivatives of $R$ with respect to $\epsilon_1$ are
extremely low and considering the scenario of $c=1$ then the
derivative will be even lower in the "walls" of the bubble in the
region where $\epsilon_1$ have high-values.


Considering now a varying $c$ due to a increasing $u_0$ then the
Dutch Equation can be written as $R=P_3\sqrt u_0$ with $P_3$ being
$P_3=\frac{2}{\epsilon}\epsilon_0\hbar\sqrt(\pi G)$ and

\begin {itemize}

\item[1)] $dR=\frac{1}{2}\frac{P_3}{\sqrt u_0}du_0$ ;

\item[2)] $dR^2=\frac{1}{4}\frac{P_3^2}{u_0}du_0^2$ .

\end {itemize}

The variation of $u_0$ could be very similar to the variation of
$\epsilon_1$ in eq 3.This can also be applied for the next case of
a varying light speed.

In the case that both $\epsilon_0$ and $u_0$ are varying then the
Dutch Equation can be written as $R=P_4 \epsilon_0 \sqrt(u_0)$
with $P_4 = \frac{2}{\epsilon} \hbar \sqrt(\pi G)$.Note that in
this case $c=\frac{1}{\sqrt(u_0\epsilon_0)}$ varies accordingly.

\begin {itemize}

\item[1)] $dR=P_4 ( 2 \sqrt(u_0) \epsilon_0 d\epsilon_0 +
\frac{1}{2} \frac{\epsilon_0}{\sqrt(u_0)}du_0)$ ;

\item[2)] $dR^2=P_4^2 ( 2 \sqrt(u_0) \epsilon_0 d\epsilon_0 +
\frac{1}{2} \frac{\epsilon_0}{\sqrt(u_0)}du_0)^2$ ;

\item[3)] $dR^2=P_4^2 \epsilon_0^2 ( 4 u_0 d\epsilon_0^2 + 2
d\epsilon_0 du_0 +  \frac{1}{4} \frac{1}{u_0}du_0^2)$ .


\end {itemize}

An interesting feature can be noted when we apply our concept of
enlarging the Bulk radius $R$ by increasing $\epsilon_1$ in the
framework of the electric and gravitational forces:

\begin {itemize}

\item[1)] gravitational force remains the same;

\item[2)] electric force looses intensity .

\end {itemize}

From (pp 12 between eq 13 and 14 in \cite{ref5}) we can derive the
relation between gravitational constants in a $4D$ and in a $5D$
spacetimes: $G_4=\frac{G_5}{8R}$ $G_5=G_4*8R$. Assuming that $G_4$
the Newton Constant is really a constant then when we "enlarge"
the Bulk we enlarge $G_5$ keeping the gravitational force $F_g =
\frac{G_4M1M2}{D_{12}^2}$ constant .Remember that for two bodies
$M1$ and $M2$ separated by a distance $D_{12}$,$R << D_{12}$.(pp 9
eq 8 in \cite{ref5}). The well known paradigm of the
$\frac{1}{D_{12}^3}$ for planetary orbits in extra dimensions
cannot be applied here because a $R$ of $10^2$ m in a localized
region of space is much smaller than a $D_{12}$ for example the
distance between Earth and Mars and then $R << D_{12}$ remains
valid. Also all the experiments to find out the presence of extra
dimensions did not reached the Planck size that occurs in natural
conditions where $\epsilon_0$ or $u_0$ or both,remains
unchanged.We must first enlarge $\epsilon_0$ or $u_0$ or both and
then verify if the extra dimensions appears "enlarged" because a
"curled up" extra dimension will be very difficult to detect.The
Gravitational Force in 3+1 dimensions is not affected by the
presence of the extra dimension whether "curled up" or "enlarged".

By the contrary the electric force between two charges separated
by the same distance $D_{12}$ is proportional to the Coulomb
Constant $K=\frac{1}{4\pi\epsilon_0}$ and if we enlarge
$\epsilon_1$ then we make $K$ shrinks.Since light speed can have a
variable value due to a varying $\epsilon_1$ a growing
$\epsilon_1$ can make the value of $c$ and $K$ shrinks.

Then in the scenario of VSL Cosmology if light speed is affected
only by $\epsilon_1$ then in the past not only light speed was
higher but also the intensity of electric force.Enlarging $R$ we
make the electric force smaller(a interesting line of reason would
be the size of $R$ to have electric and gravitational forces with
the same intensity.)

If light speed is affected only by $u_0$ electric and
gravitational forces are unaffected.A future study would be enable
to discover the scenario that better describes a changing light
speed.

Also note that if light speed varies then the $g_{tt}$ or $g_{00}$
component of spacetime metric tensor of General Relativity is
affected due to the derivatives of these components.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The Kalbermann-Halevi Solution of the Einstein Field Equations for Dark Matter-German(Zvi) Kalbermann,Hai Halevi}
\indent\indent

Our point of view as stated before relies upon geometrical beauty
of the Manyfold Universe between chemical equivalence between Dark
Matter and ordinary matter(abstract pp 2,4 and fig 1 in
\cite{ref1}) and in the small size of the Bulk that acts as a
geometrical trapping mechanism to keep matter and SM fields in the
Brane eliminating the need of exotic trapping mechanisms (pp 2,3
and 5 in \cite{ref3}). We will now introduce the ansatz that suits
well in the Manyfold Universe point of view and may explain the
behaviour of Dark Matter:The Correct Einstein Field Equation of
General Relativity that can describe mathematically the beauty of
the ADDK Manyfold Universe was developed by German (Zvi)
Kalbermann and Hai Halevi from Jerusalem University,Tel Aviv
University and Rehovot University in Israel The Kalbermann-Halevi
ansatz \cite{ref3}. Kalbermann shows(pp 8 eq 8 in \cite{ref3})
that a signal in the Bulk travels in $2,5*10^{-10}$ seconds a
distance equivalent to 326 million light years in the Brane. This
ansatz explains exactly the behaviour of Dark Matter: Imagine a
new star formed at 326 million light years away.Its gravity will
reach us in $2,5*10^{-10}$ seconds affecting our local
neighbourhoods but in the first 326 million years of life the star
would appear to us as a Dark Star or a MACHO star until the
arrival of the first photons to our local neighbourhoods to make
the star "shine"(pp 4,5 in \cite{ref1}).This does not means that
gravity propagates at "Superluminal" speeds:it does mean that
gravity can take the Bulk shortcuts.Consider a gravity signal
entering in the "throat" of the Origami ,it will travel across the
"throat" reaching the other side of the Manyfold at milimeters of
distance while light and SM particles and fields travelling across
the Brane must take the 326 million years to cover the distance to
the other side of the fold. Considering Macroscopic Bodies we
cannot accelerate to "Superluminal" speeds due to the limitations
in energy requirements but also due to the G-forces that would
destroy the integrity of the body.

The Kalbermann-Halevi ansatz is given by the following equation
(pp 4 eq 3 in \cite{ref3})

\begin{equation}  \label{eq5}
ds^2 = a(R)dt^2 - b(R)dR^2 - c(R)dl^2
\end{equation}

where $R$ is the Bulk dimension and $dl^2$ is the line element of
the Brane.

A more specifical example can be written as (pp 7 eq 7 in
\cite{ref3}):

\begin{equation}  \label{eq6}
ds^2 = (1+kR^2)dt^2 - b(R)dR^2 - e^{-k(R^2)/2}dl^2
\end{equation}

This ansatz have a generic $b(R)$

Solving the Null-Like Geodesics for the equation above and
considering that $R$ have small derivatives and $\frac{dR}{dt}$ is
close to zero we easily see how Kalbermann arrived at the result
of 326 million light years in $2,5*10^{-10}$ seconds(pp 8 eq 8 in
\cite{ref3}).

Solving the Null-Like with respect to the $dl^2$ we have:

\begin{equation}  \label{eq9}
(\frac{dl}{dt})^2 = \frac{a(R)}{c(R)}[1 -
\frac{b(R)}{a(R)}(\frac{dR}{dt})^2]
\end{equation}

\begin{equation}  \label{eq9}
(\frac{dl}{dt})^2 = \frac{(1+kR^2)}{c(R)}[1 -
\frac{b(R)}{(1+kR^2)}(\frac{dR}{dt})^2]
\end{equation}


The analysis of the equation above shows that
$\frac{(1+kR^2)}{c(R)} = (1+kR^2)e^{k(R^2)/2}$ and since
$k=10^{62}$ (see pp 7 in \cite{ref3}) then $\frac{(1+kR^2)}{c(R)}
>> 1$ (making $c=1$ in the Ansatz of
Kalbermann-Halevi).$\frac{b(R)}{(1+kR^2)}(\frac{dR}{dt})^2$ must
also have a small value to enhance the "Superluminal" properties
of the shortcut.



We will now study the behaviour of the energy density $G_{00}$
Einstein Tensor in this ansatz when we enlarge the size of the
Bulk from $10^{-35}$m to $10^2$ m allowing matter and SM fields to
use the Bulk Shortcuts to travel light years in seconds and we
will show that $G_{00}$ remains low and affordable.

The energy density $G_{00}$ in Kalbermann-Halevi ansatz is given
by\cite{ref4} Although we use the $G_{00}$ for illustrative
purposes the final considerations will use the $G^{00}$

\begin{equation}  \label{eq7}
G_{00}=\frac{3a}{4b^2c}[(\frac{db}{dR}\frac{dc}{dR})-2(\frac{d^2c}{dR^2}b)]
\end{equation}

Note that this $G_{00}$ is different than the one presented in the
original Kalbermann work (pp 5 eq 4 in \cite{ref3}) and since our
$G_{00}$ is the correct one (see also the Acknowledgements note in
this work) it must replace the $G_{00}$ depicted in the Kalbermann
original work.Also all the others $G_{pq}$ must be replaced too.

We are looking for an ansatz that retains the "Superluminal"
behaviour (pp 8 eq 8 in \cite{ref3}) and (pp 3,16 in \cite{ref1})
and provides a low and affordable energy density whether the Bulk
have the size of $10^{-35}$m or $10^2$m.

We must find the expression for $b(R)$ that will provide a zero
energy density $G_{00} = 0$ and from this expression we will
deduce the one for low energy densities

Then

\begin{equation}  \label{eq8}
G_{00}=\frac{3a}{4b^2c}[(\frac{db}{dR}\frac{dc}{dR})-2(\frac{d^2c}{dR^2}b)]=0
\end{equation}

when

\begin{equation}  \label{eq9}
b(R)=(kR)^2e^{-kR^2}
\end{equation}

rewriting the Kalbermann-Halevi ansatz we have:

\begin{equation}  \label{eq10}
ds^2 = (1+kR^2)dt^2 - (kR)^2e^{-kR^2}dR^2 - e^{-k(R^2)/2}dl^2
\end{equation}

Note that in this ansatz $b(R)$ is not equal to $(kR)^2e^{-kR^2}$
otherwise $G_{00}$ would be zero. $b(R)\simeq(kR)^2e^{-kR^2}$ to
make $G_{00}\simeq0$ but of course not null.

Also note that a $b(R)\simeq(kR)^2e^{-kR^2}$ will have a low value
increasing the "Superluminal" features of the Null-Like Geodesics
as we desire due to the nature of $(kR)^2e^{-kR^2}$

\begin{equation}  \label{eq9}
(\frac{dl}{dt})^2 = \frac{(1+kR^2)}{e^{-k(R^2)/2}}[1 -
\frac{(kR)^2e^{-kR^2}}{(1+kR^2)}(\frac{dR}{dt})^2]\dashrightarrow
(\frac{dl}{dt})^2 = (1+kR^2){e^{k(R^2)/2}}[1 -
\frac{(kR)^2}{e^{kR^2}(1+kR^2)}(\frac{dR}{dt})^2]
\end{equation}

\begin{equation}  \label{eq9}
\frac{(kR)^2e^{-kR^2}}{(1+kR^2)}\simeq0\dashrightarrow
(\frac{dl}{dt})^2 = (1+kR^2){e^{k(R^2)/2}}
\end{equation}

The equation above outlines the Kalbermann point of view in pp 8
eq 8 in \cite{ref3})


note that this ansatz retains the Superluminal behaviour  and have
a null $G_{00}$ energy density whether the Bulk size(dimension
$e$) is of $10^{-35}$m or $10^2$ meters. Also as in the original
Kalbermann-Halevi (pp 7 eq 7 in \cite{ref3}) it reduces to
ordinary special relativity ansatz when $R=0$

Of course we imagine that our unknown physical process to enlarge
the Bulk(uncurling the extra curled up dimensions) would require
energy then our  ansatz with $G_{00}=0$ is a mathematical
curiousity mentioned only to demonstrate that GR "allows" a ansatz
of null-energy when "uncurling" the extra dimensions from
$10^{-35}$m to $10^2m$ We are expecting that this process to
uncurl the extra dimensions to macroscopic size needed for
spacetime shortcuts requires a $G_{00}$ different than zero but
low and affordable. At least we know that we can manipulate the
value of b to get a $G_{00}$ equal to or close to zero
independently of the size of the extra dimension. For the future
energy density requirements we will use $G^{00}$ instead of
$G_{00}$


A more realistic ansatz that would enlarge the Bulk from
$10^{-35}$m to $10^2$m would be given by

\begin{equation}  \label{eq11}
G_{00}=\frac{3a}{4b^2c}[(\frac{db}{dR}\frac{dc}{dR})-2(\frac{d^2c}{dR^2}b)]=\frac{1}{k}
\end{equation}

The $k$ in all these equations is given by $k=10^{62}$(pp 7 in
\cite{ref3}) and if we make $G_{00}=\frac{1}{k}$ we would have a
very low energy density($10^{-62}$) ideal for our "Superluminal"
ansatz. Note that integrating the energy density over the Bulk
volume(since the Brane dimensions do not enter in the expression
for $G_{00}$) in these conditions the energy needed for this
process would still be very low even considering that the Bulk
volume will raise by a factor of $10^{37}$ times.

We have $a$ and $c$ fixed and explicitly written (eq 6)being $b$ a
variable.In this case the value of $b$ will fall near eq 9 since
$G_{00}$ will fall near $0$.

The contravariant energy density $G^{00}$ for the
$G_{00}=\frac{1}{k}$ would be given by:

\begin{equation}  \label{eq12}
G^{00}=\frac{3}{4ab^2c}[(\frac{db}{dR}\frac{dc}{dR})-2(\frac{d^2c}{dR^2}b)]=\frac{1}{a^2k}
\end{equation}

Note that a large $R$ for Bulk radius will maximize the value of
$a$ lowering the energy density as the Bulk radius
increase(Fundamental to allow Macroscopic Bodies entering in the
Bulk "throat") keeping valid our approximation of $b$ to eq 9..

Rewriting the Kalbermann-Halevi ansatz using the Bulk radius $R$
from the Dutch Equation(case $c=1$) we should expect for:

\begin{equation}  \label{eq13}
ds^2 = (1+k\frac{4\pi\epsilon_1G\hbar^2}{\epsilon^2})dt^2 -
(k^2\frac{4\pi\epsilon_1G\hbar^2}{\epsilon^2})e^{-k\frac{4\pi\epsilon_1G\hbar^2}{\epsilon^2}}
\frac{1}{4}\frac{\frac{4\pi G\hbar^2}{\epsilon^2}
}{\epsilon_1}d\epsilon_1^2 -
e^{-k(\frac{4\pi\epsilon_1G\hbar^2}{\epsilon^2})/2}dl^2
\end{equation}

and a variable $c$ for a varying $\epsilon_0$ :

\begin{equation}  \label{eq14}
ds^2 = (1+k\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2})dt^2 -
(k^2\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2})e^{-k\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2}
}\frac{4\pi G\hbar^2u_0}{\epsilon^2}d\epsilon_1^2 -
e^{-k(\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2} )/2}dl^2
\end{equation}

for a varying $u_0$

\begin{equation}  \label{eq15}
ds^2 = (1+k\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2})dt^2 -
(k^2\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2})e^{-k\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2}
}\frac{1}{4}\frac{\frac{4\pi
G\hbar^2\epsilon_0^2}{\epsilon^2}}{u_0}du_0^2 -
e^{-k(\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2} )/2}dl^2
\end{equation}

for both varying $\epsilon_1$ and $u_0$

\begin{equation}  \label{eq16}
ds^2 = (1+k\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2})dt^2 -
(k^2\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2})e^{-k\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2}
}\frac{4}{\epsilon} \pi G \hbar^2 \epsilon_1^2 ( 4 u_0
d\epsilon_1^2 + 2 d\epsilon_1 du_0 + \frac{1}{4}
\frac{1}{u_0}du_0^2) -
e^{-k(\frac{4\pi\epsilon_1^2G\hbar^2u_0}{\epsilon^2} )/2}dl^2
\end{equation}


The four equations above outline the physical beauty of our
model:a General Relativity spacetime ansatz "engineered" in
function of the physical constants in a inspiration from Millis in
\cite{ref6} and Magueijo in abstract of \cite{ref7} using the
Dutch Equation ( pp 12 eq 14 in \cite{ref5}).


Note that when $R=0$ this reduces to a SR ansatz.

The equations above were written using the terms $P_1$,$P_2$,$P_3$
and $P_4$ explicitly written to better illustrate our point of
view.A algebraic sample form using $P_1$,$P_2$,$P_3$ and $P_4$ to
simplify the expressions for $G^{00}$ and $G_{00}$ would be given
by:

\begin{equation}  \label{eq17}
ds^2 = (1+kP_1^2\epsilon_1)dt^2 -
(k^2P_1^2\epsilon_1)e^{-kP_1^2\epsilon_1}\frac{1}{4}\frac{P_1^2}{\epsilon_1}d\epsilon_1^2
- e^{-k(P_1^2\epsilon_1)/2}dl^2
\end{equation}

for $c=1$ and

\begin{equation}  \label{eq18}
ds^2 = (1+kP_2^2\epsilon_1^2)dt^2 -
(k^2P_2^2\epsilon_1^2)e^{-kP_2^2\epsilon_1^2}P_2^2d\epsilon_1^2 -
e^{-k(P_2^2\epsilon_1^2)/2}dl^2
\end{equation}

for a variable $c$ in a varying $\epsilon_1$ and

\begin{equation}  \label{eq19}
ds^2 = (1+kP_3^2u_0)dt^2 -
(k^2P_3^2u_0)e^{-kP_3^2u_0}\frac{1}{4}\frac{P_3^2}{u_0}du_0^2 -
e^{-k(P_3^2u_0)/2}dl^2
\end{equation}

for a variable $c$ in a varying $u_0$ and

\begin{equation}  \label{eq20}
ds^2 = (1+kP_4^2\epsilon_1^2 u_0)dt^2 - (k^2P_4^2\epsilon_1^2
u_0)e^{-kP_4^2\epsilon_1^2 u_0}P_4^2\epsilon_1^2(4 u_0
d\epsilon_1^2 + 2 d\epsilon_1 du_0 +  \frac{1}{4}
\frac{1}{u_0}du_0^2)- e^{-k(P_4^2\epsilon_1^2 u_0)/2}dl^2
\end{equation}

variable $c$ from both varying $\epsilon_1$ and $u_0$ .


The $G_{00}$ and $G^{00}$ for the case $c=1$ would be given by:

\begin{equation}  \label{eq21}
G_{00}=\frac{3a}{4b^2c}[(\frac{db}{\frac{1}{2}\frac{P_1}{\sqrt\epsilon_1}d\epsilon_1}\frac{dc}{\frac{1}{2}\frac{P_1}{\sqrt\epsilon_1}d\epsilon_1})-2(\frac{d^2c}{
\frac{1}{4}\frac{P_1^2}{\epsilon_1}d\epsilon_1^2}b)]
\end{equation}

\begin{equation}  \label{eq22}
G^{00}=\frac{3}{4ab^2c}[(\frac{db}{\frac{1}{2}\frac{P_1}{\sqrt\epsilon_1}d\epsilon_1}\frac{dc}{\frac{1}{2}\frac{P_1}{\sqrt\epsilon_1}d\epsilon_1})-2(\frac{d^2c}{
\frac{1}{4}\frac{P_1^2}{\epsilon_1}d\epsilon_1^2}b)]
\end{equation}

and for the case of a variable $c$ due to a varying $\epsilon_1$
by:

\begin{equation}  \label{eq23}
G_{00}=\frac{3a}{4b^2c}[(\frac{db}{P_2d\epsilon_1}\frac{dc}{P_2d\epsilon_1})-2(\frac{d^2c}{P_2^2d\epsilon_1^2}b)]
\end{equation}

\begin{equation}  \label{eq24}
G^{00}=\frac{3}{4ab^2c}[(\frac{db}{P_2d\epsilon_1}\frac{dc}{P_2d\epsilon_1})-2(\frac{d^2c}{P_2^2d\epsilon_1^2}b)]
\end{equation}

for a varying $u_0$ by:

\begin{equation}  \label{eq25}
G_{00}=\frac{3a}{4b^2c}[(\frac{db}{\frac{1}{2}\frac{P_3}{\sqrt
u_0}d u_0}\frac{dc}{\frac{1}{2}\frac{P_3}{\sqrt u_0}d
u_0})-2(\frac{d^2c}{ \frac{1}{4}\frac{P_3^2}{u_0}d u_0^2}b)]
\end{equation}

\begin{equation}  \label{eq26}
G^{00}=\frac{3}{4ab^2c}[(\frac{db}{\frac{1}{2}\frac{P_3}{\sqrt
u_0}d u_0}\frac{dc}{\frac{1}{2}\frac{P_3}{\sqrt u_0}d
u_0})-2(\frac{d^2c}{ \frac{1}{4}\frac{P_3^2}{u_0}d u_0^2}b)]
\end{equation}

and for a varying $\epsilon_1$ and $u_0$ by:

\begin{equation}  \label{eq27}
G_{00}=\frac{3a}{4b^2c}[(\frac{db}{P_4 ( 2 \sqrt(u_0) \epsilon_1
d\epsilon_1 + \frac{1}{2} \frac{\epsilon_1}{\sqrt(u_0)}du_0)
}\frac{dc}{P_4 ( 2 \sqrt(u_0) \epsilon_1 d\epsilon_1 + \frac{1}{2}
\frac{\epsilon_1}{\sqrt(u_0)}du_0)})-2(\frac{d^2c}{P_4^2
\epsilon_1^2 ( 4 u_0 d\epsilon_1^2 + 2 d\epsilon_1 du_0 +
\frac{1}{4} \frac{1}{u_0}du_0^2)}b)]
\end{equation}

\begin{equation}  \label{eq28}
G^{00}=\frac{3}{4ab^2c}[(\frac{db}{ P_4 ( 2 \sqrt(u_0) \epsilon_1
d\epsilon_1 + \frac{1}{2} \frac{\epsilon_1}{\sqrt(u_0)}du_0)
}\frac{dc}{P_4 ( 2 \sqrt(u_0) \epsilon_1 d\epsilon_1 + \frac{1}{2}
\frac{\epsilon_1}{\sqrt(u_0)}du_0)})-2(\frac{d^2c}{P_4^2
\epsilon_1^2 ( 4 u_0 d\epsilon_1^2 + 2 d\epsilon_1 du_0 +
\frac{1}{4} \frac{1}{u_0}du_0^2)}b)]
\end{equation}



These $G_{00}$ and $G^{00}$ are similar to the ones used in eq 11
and 12 giving the result of eq 8 since $\frac{1}{k}$ or
$\frac{1}{a^2k}$ have values very close to zero due to a large $a$
in the "bubble" "walls" and due to $k=10^{62}$

This illustrates how a stress energy momentum tensor of the
Einstein Field Equations of General Relativity can be "engineered"
from a "vacuum polarization" of a variable light speed or a
variable electric permeability of the vacuum.(Millis in
\cite{ref6} and Magueijo in abstract of \cite{ref7})

By enlarging for the eletric permittivity in vacuum we will
enlarge the size of the Extra Dimensions allowing matter and SM
fields to travel to the Spacetime Shortcuts of the Manyfold
Universe.But can this be really done?

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The Variation of $\epsilon_0$ and $u_0$ to enlarge the Extra Dimension-Martin Tajmar and Clovis Jacinto de Matos}
\indent\indent Martin Tajmar from Austria and Clovis Jacinto de
Matos from Portugal are two scientists of ESA(European Space
Agency) working for ESTEC(European Space Technology and
Engineering Center) that for years dedicated their lives to study
anomalous phenomena in Supercondutors.\cite{ref9,ref10}

The studied why the gravitomagnetic field of a Superconductor in
rotation is of the order of(eq 5 in \cite{ref9})

\begin{equation}  \label{eq5}
B_g = 1,85 * 10^{-5}*w
\end{equation}

while the gravitomagnetic field of Earth(a entire Planet much more
massive than a Superconductor is of the order of(eq 7 in
\cite{ref9})

\begin{equation}  \label{eq5}
B_g = 3,19 * 10^{-35}*w
\end{equation}

What could be the cause of such high gravitomagnetic fields of
magnitude order of $10^{30}$ known a Tate results??(\cite{ref9}
before eq 6)

Tajmar and Matos suggests a abnormal coupling between
Electromagnetism and Gravitation for Quantum Materials of
Superconductors and theoretizes different values of $G$ or
$c$(exactly what we need to enlarge the Bulk:different constants .
These constants would be drastically different in Superconductors.
However $G$ different would imply in reduction weight which is not
observed. But a different refraction index(a variable $c$) being
slowed down as Matos and Tajmar mentions a speed of light of $3,9*
10^{-7}$ $m/s$ would be needed to explain the Tate
abnormally(\cite{ref9} after eq 7). Matos and Tajmar mentions
experiments carried by other researchers in which the speed of
light was reduced by seven orders of magnitude or even the speed
of light is completely stopped down(a paradox since by special
relativity light cannot stop) in a Bose-Einstein-Condensator made
of Sodium atoms.According to Matos and Tajmar this exotic
behaviour could explain why rotating Quantum Materials could
produce Non-Classical Gravitomagnetic fields even at classical
angular velocities solving the Tate abnormally. But can Quantum
Materials like Niobium Superconductors affects the Spacetime
Geometry and enlarge the Planck Extra Dimensions according to the
Dutch Equation??

Tajmar and Matos mentions another Tate experiment with Niobium
Superconductor Rings(pp 3 in \cite{ref10}) that affects the
Spacetime Geometry in a way that may be useful to enlaege the Bulk
according to the Dutch Equation.

Starting with the Classical Coupling between Gravity and
Electromagnetism given by(pp 3 eq 2 in \cite{ref10}):

\begin{equation}  \label{eq20}
|k|=\frac{\mu_{0g}}{\mu_0}\frac{m}{e}
\end{equation}

where $\mu_{0g}$ is the Gravitomagnetic Permeability of Vacuum and
${\mu_0}$ is the Magnetic Permeability of Vacuum $m$ is the
electron mass and $e$ is the electron charge.

This Coupling is very small and plays no role in laboratory
experiments(pp 3 in \cite{ref10})

However the interesting point of view proposed by Tajmar and Matos
is the fact that a Superconductor in Rotation is no longer tied to
3D+1 Spacetime:As a matter of fact in (pp 5 in \cite{ref10}) both
authors asks if Spacetime is really 4D for Quantum Systems.

They propose a Fractal-Spacetime of $D$ Dimensions for Quantum
Rotating Superconductors(pp 6 in \cite{ref10}) with even
non-integer dimensionality but we will assume that this Fractal
Spacetime is really a Extra Dimensional Manyfold Universe physical
measure.(It would be very had to conceal General Relativity
formalism of Ricci Curvature Tensors and Einstein Field Equations
using scripts for integer dimensions with a dimension that is a
non-integer script).But the idea of Matos and Tajmar is very
important and very interesting for the study of Spacetime
Shortcuts to reach Remote Parts of the Universe:Macroscopic
Quantum Systems(eg Niobium Rotating Superconductors) can open the
key to the Extra Dimensional Spacetime.(pp 5,6,7,8,9,10 and 11 in
\cite{ref10}).At least we have a Macroscopical Object that can
exntends beyond the $4D$ or $3+1$ Spacetime.For the first time we
have experimental work on Extra Dimensional Physics beyond all the
theoretical BraneWorld models.( Conclusion pp 11 in \cite{ref10})

They propose a $G_D$ gravitational constant defined as( eq 14 pp 6
in \cite{ref10})

\begin{equation}  \label{eq20}
\frac{G_D}{G_4} = l_c^{D-4}
\end{equation}

$l_c$ is the Compactification Lenght of the Extra Spatial
Dimension.(In our case is of the order of Planck Lenght)

Making the $D$ Dimensional spacetime $D=5$ which means to say
$3+1$ ordinary Spacetime of $3$ Space Dimensions $1$ Time
Dimension and $1$ Extra Planck Dimension

\begin{equation}  \label{eq20}
\frac{G_5}{G_4} = l_c^{5-4}\overrightarrow{}\frac{G_5}{G_4} = l_c
\end{equation}

They propose a $G_D$ Gravitational constant of $2,55 * 10^{28}$
$\frac{N*m^2}{Kg^2}$ (eq 17 pp 6 in \cite{ref10}) to explain the
abnormal Electromagnetic and Gravitation Coupling found in Niobium
Rotating Superconductors of $36$ orders of magnitude higher than
in Classical Systems.(pp 11 in \cite{ref10})

We will concentrate ourselves in the fact that a Superconductor
can open the way to the Higher Dimensional Spacetime and enlarge
the Bulk according to the Dutch Equation.

We know that $\frac{G_5}{G_4} = l_c$ is compatible with our
definition for $G_5$ according to the Dutch Equation.

The $G_5$ according to the Dutch Equation is

\begin{equation}  \label{eq20}
G_5 = G_4 * 8*R\overrightarrow{}\frac{G_5}{G_4} =
8*R\overrightarrow{}\frac{G_5}{G_4} = l_c
\end{equation}

$R$ is the radius of the Extra Dimension..note the similarity
between $R$ and $l_c$.Note also that their $G_D$ have the
dimensionality of a $G_4$ but we know that a $G_D$ must have also
the dimensionality of $l_c$ or $R$ in our case. But what is more
important:Their $G_D$ is larger than $G_4$ and applying their
$l_c$ our case of the Dutch Equation we would have the results of
a larger $R$.Working with a $D=5$ and a reasonable large $R$ we
would have a

\begin{equation}  \label{eq20}
G_5 = G_4 * 8*R\overrightarrow{}G_5=G_4*l_c
\end{equation}

They claims that the Spacetime around a Superconductor is not $4D$
to explain the difference of $36$ orders of magnitude between
Electromagnetic and Gravitational coupling around a Rotating
Superconductor.(pp 11 in \cite{ref10})

The Electromagnetic and Gravitational coupling for Rotating
Superconductors can be given by:(pp 3 eq 2 and pp 6 eq 16 without
fine structure constants in \cite{ref10} because we prefer the
Gravitomagnetic permeability of vacuum by reasons that we will
explain)

\begin{equation}  \label{eq20}
|k^D|=\frac{\mu_{0g}^D}{\mu_0}\frac{m}{e}
\end{equation}

in case of $D=5$

\begin{equation}  \label{eq20}
|k^5|=\frac{\mu_{0g}^5}{\mu_0}\frac{m}{e}
\end{equation}


Look that $|k^5| > |k|$ in agreement that Spacetime around a
Rotating Superconductor have a Coupling larger that Classical
ordinary Spacetime due to a larger size of the Extra Dimension $R$
or $lc$, and a larger Gravitational Constant $G_5 > G_4$.($G_5 =
G_4
* 8*R\overrightarrow{}G_5=G_4*l_c$).

Then we can see how the Dutch Equation can increase the
Gravitational Constant in a $N$-Dimensional Spacetime affecting
the Coupling by enlarging $R$.But exactly what causes the
enlargement of the Bulk??What causes the enlargement of $R$ ??

Working now with the Gravitomagnetic permeability of vacuum(pp 3
in \cite{ref10})

\begin{equation}  \label{eq20}
\mu_{0g}=\frac{4*\pi * G}{c^2}
\end{equation}

\begin{equation}  \label{eq20}
|k|=\frac{\mu_{0g}}{\mu_0}\frac{m}{e}\dashrightarrow|k|=\frac{\frac{4*\pi
* G}{c^2}}{\mu_0}\frac{m}{e}\
\end{equation}

\begin{equation}  \label{eq20}
|k|=\frac{\mu_{0g}}{\mu_0}\frac{m}{e}\dashrightarrow|k|=\frac{4*\pi
* G}{\mu_0 * c^2}\frac{m}{e}\
\end{equation}

But since $c^2 = \frac{1}{e_0 * \mu_0}$

\begin{equation}  \label{eq20}
|k|=\frac{\mu_{0g}}{\mu_0}\frac{m}{e}\dashrightarrow|k|=4 \pi
 G e_0 \frac{m}{e}\
\end{equation}

Then we can say that the Coupling between Electromagnetism and
Gravity can be given by:

\begin{equation}  \label{eq20}
|k|=4 \pi G e_0\frac{m}{e}\
\end{equation}

\begin{equation}  \label{eq20}
|k^5|=4 \pi G_5 e_0^{5}\frac{m}{e}\dashrightarrow|k^5|=4 \pi G_4
 8R e_0^{5}\frac{m}{e}\
\end{equation}


If $e_0$ and $u_0$ from $e_0$ and $u_0$ to $e_0^5$ and $u_0^5$
varies in the Spacetime around a Rotating Superconductor then $R$
varies and $G_5$ varies too.(If $e_0$ varies then the
Gravitational fine structure constant will vary too).(pp 3,6 in
\cite{ref10}).



\begin{equation}  \label{eq20}
|k^5|=4 \pi G_4 8R e_0^{5} \frac{m}{e} \dashrightarrow|k^5|=4 \pi
G_4  8 (\sqrt\frac{4\pi
G\hbar^2}{\epsilon^2}\epsilon_0^5\sqrt{u_0^5}) e_0^{5}
\frac{m}{e}\
\end{equation}


A large $u_5$ can make $|k_5| > |k|$ .Then a Physical model of the
Dutch Equation able to enlarge the Bulk from the Planck Size to
Macroscopical one according to the Rotating Superconductor Model
explain the abnormally large Coupling of $10^{36}$ orders of
magnitude implies in a enlargement of $e_0$ and $u_0$ according to
(pp 11 in \cite{ref10}).Note also that a very large $e_0$ and
$u_0$ can make light speed drop by large values or even slow
down.(\cite{ref9} after eq 7).

Tajmar and Matos demonstrated the validity and reality of the
Dutch Equation.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The Tate Effect in Cooper pairs of Rotating Superconductors.}
\indent\indent In the previous section we pointed out the
importance of the point of view advocated by Martin Tajmar and
Clovis Jacinto de Matos\cite{ref9,ref10} that a Superconductor is
no longer tied to our $3+1$ Spacetime and extends over Higher
Dimensional Space.This can be used to "probe" experimentally
BraneWorld considering that the fractal Dimension of Matos-Tajmar
is a real integer Extra Dimension for the reasons we explain in
the previous section. We present here the correct explanation for
the Tate Anomally when measuring the mass of the Cooper Pairs in
function of a Extra Dimension enlarged by the Dutch Equation.

Tajmar and Matos defines the Coupling between Eletromagnetics and
Gravity using the Gravitational Fine Structure Constant as: (pp 3
eq 2 in \cite{ref10}).

\begin{equation}  \label{eq20}
|k|=\frac{a_{g}}{a}\frac{e}{m}
\end{equation}

$a_{g}$ is the Gravitational Fine Structure Constant defined as:

\begin{equation}  \label{eq20}
a_{g}=\frac{G  m^2}{\hbar * c}\dashrightarrow a_{g}=\frac{G
m^2}{\hbar * \sqrt{\frac{1}{e_0  \mu_0}} }
\end{equation}

and $a$ is the Electromagnetic Fine Structure Constant defined as:

\begin{equation}  \label{eq20}
a=\frac{1}{4 \pi  \epsilon_0} \frac{e^2}{\hbar  c}\dashrightarrow
a=\frac{1}{4 \pi  \epsilon_0}\frac{e^2}{\hbar
* \sqrt{\frac{1}{e_0  \mu_0}} }
\end{equation}

\begin{equation}  \label{eq20}
|k|=\frac{a_{g}}{a}\frac{e}{m}\dashrightarrow\frac{\frac{G
m^2}{\hbar  c}}{\frac{1}{4 \pi  \epsilon_0}\frac{e^2}{\hbar
c}}\frac{e}{m}
\end{equation}

\begin{equation}  \label{eq20}
|k|=\frac{a_{g}}{a}\frac{e}{m} \dashrightarrow |k|=\frac{\frac{G
m^2}{\hbar  c}\dashrightarrow a_{g}=\frac{G  m^2}{\hbar
\sqrt{\frac{1}{e_0  \mu_0}} }}{\frac{1}{4 \pi
\epsilon_0}\frac{e^2}{\hbar  c}\dashrightarrow a=\frac{1}{4 \pi
 \epsilon_0}\frac{e^2}{\hbar
 \sqrt{\frac{1}{e_0  \mu_0}} }}\frac{e}{m}
\end{equation}

Solving the algebraic expressions we arrive at the following
results:

\begin{equation}  \label{eq20}
\frac{a_{g}}{a} = 4 \pi  \epsilon_0  G  \frac{m^2}{e^2}
\end{equation}


\begin{equation}  \label{eq20}
|k|=\frac{a_{g}}{a}\frac{e}{m}\dashrightarrow |k|= 4 \pi
\epsilon_0  G  \frac{m^2}{e^2}\frac{e}{m} \dashrightarrow |k|= 4
\pi  \epsilon_0  G  \frac{m}{e}
\end{equation}

In our previous section we defined the $5D$ Coupling as $|k^5|= 4*
\pi * \epsilon_0^5 * G^5 * \frac{m}{e} $ where $G^5$ was the $5D$
Gravitational Constant and $\epsilon_0^5$ was the enlarged eletric
permittivity and we observed that $|k^5|>|k|$ to explain the
abnormal large Quantum Coupling. According to Matos and Tajmar a
Superconductor is not tied to $3+1$ Spacetime and can "probe"
Extra Dimensional space(pp 5 and pp 6 between eqs 15 to 16 in
\cite{ref10}).

We consider here the Tajmar-Matos Fractal Dimension as a Physical
Integer Dimension since the dimension mentioned of $D=3.94$(pp 7
eq 21 in \cite{ref10}) would mean a fraccionary
Dimension(non-integer Dimension) difficult to conceal with the
formalism of Einstein General Relativity with integer Dimensions
in the Christoffel Symbols etc. But Matos and Tajmar had a
excellent idea:the idea that a Superconductor can open the door to
Higher Dimensional Spacetime more efficiently that Hadron TeV
Colliders.

We know from our previous works that the
Eletromagnetic-Gravitational Coupling can be written as

\begin{equation}  \label{eq20}
|k^5|= 4 \pi  \epsilon_0^5  G^5  \frac{m}{e}
\end{equation}

with $G_5=G_4*8*R$ and eq 14 pg 6 of \cite{ref10} with $D=5$ and
$l_c=8*R$

This Enlarged Coupling will affect the Tate Anomally is the result
of the fact that the Superconductor do not move in ordinary $3+1$
Spacetime and can access Higher Dimensions(pp 5 and 6 in
\cite{ref10}).This is the most important feature in Matos and
Tajmar studies.

Tajmar and Matos says the mass of the Cooper Pair in a Rotation
Superconductor is higher than expected due to a "Fractal
Dimension".We consider here the Extra Dimension of the Manyfold
Universe and we proof that this Dimension can enlarge the mass of
the Cooper Pair.Again we want to say that the idea of a Rotating
Superconductor accessing Higher Dimensional Spacetime is
remarkable and is perhaps the only way to test BraneWorlds in
Laboratory.

Writing the Eletromagnetic and Gravitational Coupling in function
of the Dutch Equation we should expect for:

\begin{equation}  \label{eq20}
|k|= 4 \pi  \epsilon_0  G  \frac{m}{e} \dashrightarrow
|k|=\frac{a_{g}}{a}\frac{e}{m}
\end{equation}

The Dutch Equation is given by:

\begin{equation}  \label{eq4}
R = \sqrt\frac{4\pi \epsilon_0^2G\hbar^2u_0}{\epsilon^2}
\end{equation}

\begin{equation}  \label{eq4}
R = \sqrt\frac{4\pi G\hbar^2}{\epsilon^2}\epsilon_0\sqrt{u_0}
\end{equation}

\begin{equation}  \label{eq20}
\frac{a_{g}}{a}=4 \pi  \epsilon_0  G  \frac{m^2}{e^2}
\end{equation}

One can easily see that the Dutch Equation in function of the
Coupling is given by:

\begin{equation}  \label{eq4}
R^2 = \frac{a_{g}}{a}\frac{\epsilon_0 \hbar^2u_0}{m^2}
\end{equation}

Remember that the Coupling raises due to the Higher Dimensional
Spacetime\cite{ref10},then $G$,$\epsilon_0$ and $u_0$
raises(lowering the light speed in the vicinity of the
Superconductor or even stopping it as in \cite{ref9} after eq 7 ).

Coupling raises due to Rotation then Dutch Equation raises the
size of the Extra Dimension:this is why we "see" the Higher
Dimensional Spacetime for the Rotating Superconductor.

Then:

\begin{equation}  \label{eq4}
\frac{a_{g}}{a}=\frac{m^2 R^2}{\epsilon_0 \hbar^2u_0}
\end{equation}

Now we can write the Eletromagnetic and Gravitational Coupling in
function of the Dutch Equation as follows:

\begin{equation}  \label{eq20}
|k|=\frac{a_{g}}{a}\frac{e}{m} \dashrightarrow |k|=\frac{m^2
R^2}{\epsilon_0 \hbar^2u_0}\frac{e}{m} \dashrightarrow |k|= 4 \pi
 \epsilon_0  G  \frac{m}{e}
\end{equation}

When the Superconductor Rotates its enlarges the size of the Extra
Dimension and also enlarges the Coupling:then we can say the Dutch
Equation and the Coupling are inter-related phenomena.

The Mass of the Cooper Pair is related to the Coupling and to the
Dutch Equation by the following equation(eq 16 pg 6 in
\cite{ref10} ).

\begin{equation}  \label{eq20}
|k|=\frac{a_{g}}{a}\frac{e}{m} \dashrightarrow
|k|=\frac{\Delta_m}{m_{the}}\frac{e}{m} \dashrightarrow
|k|=\frac{m^2 R^2}{\epsilon_0 \hbar^2u_0}\frac{e}{m}
\end{equation}

\begin{equation}  \label{eq20}
\Delta_m = m_{exp} - m_{the}
\end{equation}

Above $m_{exp}$ is the experimental measure of the mass of the
Cooper Pair and $m_{the}$ is the theoretical value predicted.We
can clearly see that the Rotation of the Superconductor enlarges
the Higher Dimensional Spacetime and raises the mass of the Cooper
Pair. Then according to Martin Tajmar and Clovis Jacinto de Matos
a Superconductor in a Higher Dimensional Spacetime can explain the
large Eletromagnetic and Gravitational Coupling and also explain
the difference measured by Tate for the mass of the Cooper
Pair(pp4 eq 5 in \cite{ref10}).

\begin{equation}  \label{eq20}
\frac{\Delta_m}{m_{the}}=\frac{m^2 R^2}{\epsilon_0 \hbar^2u_0}
\end{equation}

Above is the relation between the Tate Anomally and the Dutch
Equation.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Martin Tajmar and Clovis Jacinto de Matos-Abnormal Gravitomagnetic Fields.}
\indent\indent

This section is almost entirely adapted from (pp 2 and pp 11 in
\cite{ref10}). with the modification from Fractal Spacetime to a
Real Spacetime of integer Extra Dimensions:

Tate showed that the Cooper Pairs in Rotating Niobium
Superconductor Rings is higher than the one predicted by theory
even including the relativistic corrections. In our analysis we
used Higher Dimensional Spacetime(instead of Matos and Tajmar
Fractal one). But the Gravitomagnetic Field is still much higher
than whats Classical General Relativity predicts for the currents
of mass involved in the Tate experiment.What is the cause of such
Abnormal Gravitomagnetic Fields??

We will still use Higher Dimensional Spacetime to explain this
large Gravitomagnetic Field.

The Non-Classical Gravitomagnetic Field is given by(eq 6 pp4 in
\cite{ref10} combined to pp 6 eq 16 in \cite{ref10}) :


\begin{equation}  \label{eq20}
B_{y} = 2w\frac{\Delta_m}{m_{the}} \dashrightarrow B_{y} =
2w\frac{a_{g}}{a} \dashrightarrow B_{y} = 2w\frac{m^2
R^2}{\epsilon_0 \hbar^2u_0}
\end{equation}

This Non Classical Gravitomagnetic Field is related to the
Abnormal Tate Cooper Pair Mass and the Enlarged Extra Dimension of
the Dutch Equation.


\section{The Challenge To Create The "Space Drive" - Marc Millis}
\indent\indent

This section outlines the most direct application of this
"spacetime metric engineering" for Macroscopic
Shortcuts:Interstellar Travel.

If we want to talk seriously about Interstellar Travel since a
shortcut in spacetime means a way to travel to distant parts of
the Universe avoiding the speed of light limitations then we must
concentrate ourselves on the efforts of NASA scientist Marc
Millis.\cite{ref6}

Actually we know that rockets are not enough for interstellar
space travel and Marc Millis proposes the use of "spacetime metric
engineering" using electromagnetism to achieve faster than light
space travel.\cite{ref6}

However we also know that "Superluminal" travel in the Brane is
impossible thinking on a realistic way:We dont need to mention all
the existing "Superluminal" theories because Marc Millis already
summarized all of them in \cite{ref6} but considering for example
a Brane Only motion (which means to say motion in ordinary
spacetime without shortcuts) that would allow us to cover 326
million light-years in $2,5*10^{-10}$ seconds;such a motion would
imply in a impossible(and incredible) speed.Even considering the
"Superluminal physics" that theoretically allow this speed (not to
mention that this physics is often regarded as "exotic" with
negative energies etc)we know that Outer Space is not empty and a
impact with a wandering asteroid or a Black Hole would destroy the
ship(or destroy the "Drive" effect in some of these
theories\cite{ref6}).Even at a "low" speeds of $100.000$
light-years in $7$ weeks in Brane Only motion for example the
impacts with hazardous objects would still deny the trip.Also
incoming photons from Cosmic Background Radiation that are
scattered everywhere across Outer Space for example would be
severely Doppler blueshifted posing a threat to the ship and the
crew members.

The Marc Millis purpose to study the so-called "Space Drives" for
Interstellar Travel is a remarkable target to be achieved but
without breaking the light speed barrier and considering
"classical" motion on the Brane Only this target is impossible to
be reached due to the time expeditures needed to reach the stars
at huge distances from Earth or the "unphysical" behaviours one
can get at "Superluminal" speeds on the Brane Only.

Taking the ADDK Model of the Manyfold Universe with gravity using
the Bulk Shortcuts of $10^{-35}$m size to travel billion light
years in seconds as our inspiration we can think about "enlarging"
these shortcuts that traps matter and SM fields on the Brane to
allow them to enter in a Bulk Shortcut of Macroscopic size to do
the same thing that gravity does.Basically we must "enlarge" the
"throat" in order to avoid the SM "bottleneck" and allows trips of
billion light years.

Of course we dont need "speeds" of $326$ million light-years in
$2,5*10^{-10}$ seconds:at this "speed" a "Space Drive" would cross
the entire known Universe in less than an hour but if we can
"engineer" a Bulk size of $10^2$ m to travel some light-years in a
couple of hours this would be more than enough for Marc Millis
goal of Interstellar Travel.

The inspiration behind this work on Macroscopic Bulk Shortcuts is
not a mathematical abstraction but really is to study the
possibility to use them as "Hyper Dimensional Space Drives" that
would allow the Marc Millis desired goal of Interstellar
SpaceFlight.


\section{Conclusion - NASA Breakthrough Propulsion Physics Program(BPP) and the 2005 World Year Of Physics}
\indent\indent

In $1996$ NASA created the Breakthrough Propulsion Physics
Program(BPP)\cite{ref8} to seriously study the scientific
possibilities of Interstellar Space Travel.The program was lead by
the Aerospace Engineer Marc Millis from John Glenn Space Center at
Lewis Field Ohio USA. Marc Millis launched the correct scientific
foundations for the so-called "Space Drive":propulsion without
propellant,"Superluminal" velocity,capability to engineer motion
through spacetime itself,possibility to artificially "engineer" a
spacetime ansatz using the "vacuum eletromagnetics" in a way that
could resemble Joao Magueijo "vacuum polarization" for variable
light speed cosmology according to our model of proposed "Space
Drive".Our model have two strong points:the confirmation by NASA
Chandra Satellite that Dark Matter exists and the hypothetical
Dark particles such as WIMPS Axions etc have never been detected
opening the possibility that the ADDK Manyfold Universe correspond
to the physical Dark Matter reality and the observed on supernovas
fact that light speed is loosing velocity as proposed by Magueijo
and others.Our "Space Drive" relies on these two experimental
"proved" facts. Unfortunately in January $2003$ NASA closed BPP
and the explanation given was the lack of physical evidences or
physical possibilities for "Superluminal" space travel.

Unfortunately there is at present moment no viable "Superluminal"
physics without problems and pathologies of "negative energy"
"exotic field" "large amounts of energy needed" "photons highly
Doppler blueshifted" "causally disconnected portions of spacetime
(aka) Horizons" "WEC NEC SEC energy conditions violations" and
many other sad but true features published in the physics
peer-review scientific literature and influencing NASA politicians
and the final termination of NASA BPP.Unfortunately we cannot
condemn or censor NASA politicians.

But perhaps the point of view launched by Nimas-Arkani Hamed,Savas
Dimopolous,Gia Dvali,Nemaja Kaloper,Szczepan W. Kowalczyk,Jorn
Mossel,German(Zvi) Kalbermann,Hai Halevi,Joao Magueijo,Marc
Millis,Martin Tajmar and Clovis Jacinto de Matos can still open a
"light in the end of the tunnel".Perhaps if a spacetime ansatz a
solution of the Einstein Field Equations of General Relativity can
be "engineered" by "vacuum polarization electromagnetics " or
other still unknown ways we may still dream on the possibility of
Interstellar Space Travel in a far distant future,opening the
feasibility for another research program with the pioneer vision
and wisdom Marc Millis created for the NASA BPP.

The point of view that Rotating Superconductors can probe the
Higher Dimensional nature of spacetime more effective than
expensive TeV Colliders deserves further investigation. The point
of view that Rotating Superconductors can probe the Higher
Dimensional nature of spacetime more effective than expensive TeV
Colliders deserves further investigation. The idea of Martin
Tajmar and Clovis Jacinto de Matos of European Space Agency is
revolutionary and new.It not only can reinforce and give physical
meaning and relevance to Higher Dimensional Physics but also can
bring the Physics of BraneWorlds from the theoretical and abstract
point of view to the Laboratory where at last Brane Models can be
tested.



The Year $2005$ will be the Year of the Centennary of Einstein
Special Theory Of Relativity and unfortunately light speed barrier
will remain invincible and unchallengeable:but how for
long?.Perhaps a "Macroscopic Spacetime Shortcut in the Manyfold
Universe" working as a "Space Drive" may change the whole picture.


\section{Acknowledgements}
\indent\indent

We would like to express the most profound and sincere gratitude
towards Professor Doctor German(Zvi)Kalbermann from Rehovot
University Israel for the comments given when checking the
GrTensorII for Maple IX results for the $G_{00}$ energy density
tensor.Also we would like to mention Paulo Alexandre Santos from
University of Aveiro Portugal for his help in getting the
GrTensorII for Maple IX solutions.Also we would like to
acknowledge Lusitania Companhia de Seguros Lisboa Portugal for the
computer and Internet facilities allowed for this work.

\section{Remarks}
\indent\indent The work arXiv.org@gr-qc/0408001 was withdrawn from
arXiv.org when we contacted the authors about the conflicting
nature between Fractal Spacetime with fraccionary dimensions and
General Relativity.The Fractal Approach of Spacetime will be
replaced by the authors with a more suitable version.But we still
keep the original version of arXiv.org@gr-qc/0408001 for
References and Bibliographic Purposes because the Tajmar-Matos
point of view is a landmark between Material Sciencies and Physics
of Extra Dimensions.

%\newpage
\begin{thebibliography}.

\bibitem{ref1}
\textit{Nima Arkani-Hamed,Savas Dimopoulos, Gia Dvali Nemanja
Kaloper; arXiv.org@hep-ph/9911386 The Manyfold Universe
JHEP(12)-2000-010}.

\bibitem{ref2}
\textit{ Roland Pease ;28 June 2001 Nature 411, 986 - 988 (2001)}.

\bibitem{ref3}
\textit{German Kalbermann;Communication through an extra dimension
arXiv.org@gr-qc/9910063  Int.J.Mod.Phys. A15 (2000) 3197-3206}.

\bibitem{ref4}
\textit{for the solutions of the Einstein Field Equations see the
GrTensorII for Maple IX outputs for one Bulk dimensions and 3 Bulk
dimensons depicted at http://www.geocities.com/loupwarp
http://www.geocities.com/loupdrive and
http://www.geocities.com/loupspeed . Also see the mentions to Dark
Matter findings by NASA Chandra Satellite}.

\bibitem{ref5}
\textit{Stefan Kowalczyk,Quinten Krijger,Maarten Van Der Ment,Jorn
Mossel,Gerben Schooneveldt,Bart Verdoen;Constraints on Large Extra
Dimensions;Department of Physics;University of Amsterdam}.

\bibitem{ref6}
\textit{Millis, M. "Challenge to Create the Space Drive," In
Journal of Propulsion and Power (AIAA), Vol. 13, No. 5, pp.
577-682, (Sept.-Oct. 1997)}.

\bibitem{ref7}
\textit{Joao Magueijo;New varying speed of light
theories,arXiv.org@astro-ph/0305457,Rept.Prog.Phys. 66 (2003) 2025
}.
\bibitem{ref8}
\textit{NASA Breakthrough Propulsion Physics Program - BPP;
http://www.grc.nasa.gov/WWW/bpp/}.


\bibitem{ref9}
\textit{Martin Tajmar,Clovis Jacinto de Matos.Extended Analysis of
Gravitomagnetic Fields in Rotating Superconductors and
Superfluids.arXiv.org@gr-qc/0406006 }.

\bibitem{ref10}
\textit{Martin Tajmar,Clovis Jacinto de Matos.Gravitomagnetic
Fields in Rotating Superconductors due to Fractal Space-Time.
arXiv.org@gr-ac/0408001 }.

\bibitem{ref11}
\textit{NASA Chandra Satellite Final Report.
http://chandra.harvard.edu/resources/faq/dmatter/dmatter-9-html }

\bibitem{ref12}
\textit{for the Dutch Equation see the Homepage of Jorn Mossel one
of the Authors from University of Amsterdam.Holland.
http://student.science.uva.nl/~jmossel/ }.

\bibitem{ref13}
\textit{for the Dutch Equation see the Homepage of Szczepan W.
Kowalczyk  one of the Authors from University of
Amsterdam.Holland. http://student.science.uva.nl/~skowalcz/ }.


\end{thebibliography}.

\end {document}.
