An introduction to general relativity and entropy bounds

Kotze, Jacques (2006-04)

Thesis (MSc)--University of Stellenbosch, 2006.


ENGLISH ABSTRACT: Entropy bounds arise from Black hole thermodynamics and are a significant departure from the conventional understanding of the information in a given region. This shift in paradigm is a consequence of the the fact that there is an unexpected relationship between the area and the entropy of a given region of spacetime. Entropy bounds are simplified formulations which are ultimately attempting to be developed into the complete and broad conjecture of the Holographic Principle. This hasn’t been achieved successfully as yet. In this thesis the aim is to introduce how the notion of an entropy bound was first suggested and it’s subsequent development into more robust formulations. The shortcomings of these conjectures are highlighted along with their strengths. A foundational introduction of the mathematical requirements for General Relativity is addressed along with an overview of Einstein’s theory of gravity. This is illustrated by showing the curvature of relative geodesics as being a consequence of gravity. This is contrasted with Newtonian theory where gravity is also shown to manifests as the curvature of relative geodesics. The working background is concluded with a discussion of Einstein’s field equations along with simple and common solutions often used and required.

AFRIKAANSE OPSOMMING: Swartgat Termodinamika impliseer grense op die entropie, en dus inligting, in ’n gegewe ruimtetyd volume, wat ’n drastiese afwyking van die tradisionele denkwyse oor inligting impliseer. Hierdie paradigma skuif het sy oorsprong in ’n onverwagte verband tussen die oppervlakte van, en entropie bevat, in ’n gegewe ruimte tyd volume. Entropie grense is eenvoudige formulerings van hierdie verwantskap wat uiteindelik beslag moet kry in die vollediger en wyer holografiese beginsel. Hierdie doelwit is nog nie bereik nie. Die doel van hierdie tesis is om die oorsprong en verdere formalisering van entropie grense te verduidelik. Beide die sterk en swak punte van die formulerings word bespreek. Algemene relatiwiteits teorie as ’n teorie van gravitasie, sowel as die wiskundige onderbou daarvan, word oorsigtelik bespreek. Die geometries onderbou van gravitasie word geillustreer aan die hand van die buiging van relatiewe geodete. Dit word met Newton se gravitasie teorie vergelyk wat ook in die buiging van relatiewe geodete gemanifesteer word. Hierdie oorsigtelike agtergrond word afgesluit met ’n oorsig van Einstein se vergelykings, asook eenvoudige en algemene oplossings wat dikwels nodig is en gebruik word.

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