Algebraic and numerical techiques in general relativity: The classification of spacetimes via the Cartan-Karlhede method and Cauchy-Characteristic matching for numerically generated spacetimes
Algebraic and numerical techiques in general relativity: The classification of spacetimes via the Cartan-Karlhede method and Cauchy-Characteristic matching for numerically generated spacetimes
This thesis concerns two distinct areas of research (i) the development of a practical set of methods for the classification of spacetimes in general relativity, and (ii) the numerical solution of the vacuum Einstein equations on null hypersurfaces.
The first part examines the Cartan-Karlhede method for determining a unique classification of algebraically distinct spacetimes. A key aspect of this method is the establishment of a set of 'standard forms' for symmetric spinors. A set of standard forms is developed, with an emphasis on the need for consistency, and reduction of computational complexity. The Cartan-Karlhede method has been incorporated into a set of programs for the computer algebra system Maple and form a general set of tools for the use of relativists. Certain inherent difficulties with the Cartan-Karlhede methods, such as the need to determine the roots of high order polynomials, are identified, along with potential alternative methods for handling these difficulties.
The second part of the thesis details the development of a Cauchy-characteristic matching (CCM) code in axisymmetry. In the CCM technique, a spacetime is evolved on two separate grids with information passed between the two. The advantage of this method is the ability to use well-developed Cauchy codes in the interior (where characteristics would tend to develop caustics) and a characteristic region which extends to null infinity, alleviating the need for artificial boundary conditions. The code which is being developed passes information in both directions across the boundary. A condition at null infinity ensures that Bondi-type slicing of the spacetime is maintained, with the advantage that the mass and news functions are thus easily identifiable.
A full description of the evolution systems in both the Cauchy and characteristic regions is given. The interface is implemented along a single r = constant surface to avoid difficulties arising from interpolation between the grids over a region. Difficulties arise in co-ordinating the evolution in each region so that the required information is provided at the boundary when it is needed, however for the given system of equations they can be surmounted in a manner consistent with the overall evolution scheme.
University of Southampton
Pollney, Denis
a78b371e-934f-4fed-8754-91db5cdeb23e
2000
Pollney, Denis
a78b371e-934f-4fed-8754-91db5cdeb23e
Pollney, Denis
(2000)
Algebraic and numerical techiques in general relativity: The classification of spacetimes via the Cartan-Karlhede method and Cauchy-Characteristic matching for numerically generated spacetimes.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
This thesis concerns two distinct areas of research (i) the development of a practical set of methods for the classification of spacetimes in general relativity, and (ii) the numerical solution of the vacuum Einstein equations on null hypersurfaces.
The first part examines the Cartan-Karlhede method for determining a unique classification of algebraically distinct spacetimes. A key aspect of this method is the establishment of a set of 'standard forms' for symmetric spinors. A set of standard forms is developed, with an emphasis on the need for consistency, and reduction of computational complexity. The Cartan-Karlhede method has been incorporated into a set of programs for the computer algebra system Maple and form a general set of tools for the use of relativists. Certain inherent difficulties with the Cartan-Karlhede methods, such as the need to determine the roots of high order polynomials, are identified, along with potential alternative methods for handling these difficulties.
The second part of the thesis details the development of a Cauchy-characteristic matching (CCM) code in axisymmetry. In the CCM technique, a spacetime is evolved on two separate grids with information passed between the two. The advantage of this method is the ability to use well-developed Cauchy codes in the interior (where characteristics would tend to develop caustics) and a characteristic region which extends to null infinity, alleviating the need for artificial boundary conditions. The code which is being developed passes information in both directions across the boundary. A condition at null infinity ensures that Bondi-type slicing of the spacetime is maintained, with the advantage that the mass and news functions are thus easily identifiable.
A full description of the evolution systems in both the Cauchy and characteristic regions is given. The interface is implemented along a single r = constant surface to avoid difficulties arising from interpolation between the grids over a region. Difficulties arise in co-ordinating the evolution in each region so that the required information is provided at the boundary when it is needed, however for the given system of equations they can be surmounted in a manner consistent with the overall evolution scheme.
Text
831141.pdf
- Version of Record
More information
Published date: 2000
Identifiers
Local EPrints ID: 464573
URI: http://eprints.soton.ac.uk/id/eprint/464573
PURE UUID: a4ef93f8-2cb3-4cfc-961e-e3690f1c356f
Catalogue record
Date deposited: 04 Jul 2022 23:48
Last modified: 16 Mar 2024 19:37
Export record
Contributors
Author:
Denis Pollney
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics