Black holes, Singularity theorems and The Global structure of Spacetime

TL;DR

This thesis provides a comprehensive review of the large-scale structure of spacetime, including black hole metrics, causal structures, singularity theorems, and exotic phenomena in general relativity.

Contribution

It offers an accessible synthesis of complex topics like black hole solutions, causality, singularities, and exotic spacetime structures, with detailed explanations and author insights.

Findings

Derivation and analysis of Schwarzschild, Reissner-Nordström, and Kerr metrics

Discussion of spacetime causality and global hyperbolicity

Explanation of singularity theorems and black hole properties

Abstract

This work is an extensive literature review focusing on a few of the important topics in the large-scale structure of spacetime. The work is a Bachelor's thesis submitted at the Institute of Theoretical Physics, University of Leipzig. The author starts the thesis by deriving the Schwarzchild metric, Reissner Nordstorm metric and discusses their properties with appropriate Penrose diagrams. The Kerr black hole is metric is assumed, and its features are examined. The causal structure of spacetime is discussed with a focus on different stages of causality on a spacetime, Cauchy surfaces, and what does it mean for spacetime to be Globally hyperbolic. Then, the author moves to Singularity theorems, where one can find an algorithm to deal with non-coordinate singularities in spacetime. A few singularity theorems are discussed in detail. Then, the asymptotic structure of spacetime is discussed, which leads to a precise definition of a Black hole and its event horizon. The Black hole area theorem by Prof. Hawking is dissected pointwise with exclusive author comments as an attempt to simplify it for a less advanced audience. After that, a few exotic propositions in General relativity like closed timelike curves and warp drives are discussed.