Unraveling the mysteries of spacetime: holographic codes and gravitational lensing

Abstract

The fabric of spacetime is the underlying structure embedding the entirety of the observable phenomena in our universe and though it has been studied in significant detail, many mysteries remain. This thesis is dedicated to studying two particular topics that arose from explorations into the nature of spacetime and is correspondingly separated into two distinct parts, namely holographic quantum error-correcting codes and gravitational microlensing.

The first part of this thesis concerns itself with the suggestion that spacetime is not fundamental but rather an emergent concept. According to the holographic principle, the fundamental degrees of freedom of a bulk spacetime are encoded on its boundary surface, which is of one dimension lower than the bulk. The AdS/CFT correspondence is the most explicit realisation of the holographic principle, forming a unique framework in which one can use concepts and techniques arising in quantum information theory to study quantum gravity. Holographic properties have been vastly explored through the novel use of tensor networks, which can be interpreted as encoders for quantum error-correcting codes. We focus our attention on the study of codes associated with holographic geometries living in higher dimensions, constructing stabiliser codes that are analogues of the famous HaPPY code [1]. We do so by considering both absolutely maximally entangled (AME) and non-AME codes noting that discrete symmetries of the polytope are always broken for AME codes in dimensions higher than two. We also explore alternate constructions of stabiliser codes for hyperbolic spaces in which the we associate the logical information with the boundary.

The second part of this thesis involves gravitational lensing, the observed astrophysical phenomena involving the propagation of light through a specific background spacetime, governed by its null geodesic equations. Utilising the expansions presented in [2], we consider gravitational lensing by a rotating, compact object (i.e an object described by the Kerr metric) in the weak deflection limit, thus assuming large astrophysical separations. We present magnification curves using point-source models for numerous geometrical configurations involving different inclinations and spins. Throughout this analysis, we discuss the plethora of applications that arise in both astrophysics and fundamental theory before introducing a more realistic model adjusted for the inclusion of extended sources with limb-darkening effects.

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Identifiers

ORCID for Marika Taylor: orcid.org/0000-0001-9956-601X

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