Exploring Spacetime and Singularities

Abstract

<p> Hawking's Singularity Theorem establishes the existence of a cosmological singularity in a spacetime for which no global assumptions about causality are made. This theory has been useful for predicting the occurrence of singularities in a spacetime without solving Einstein's field equation. This paper is an exposition of the tools and some of the theory required to prove and apply Hawking's theorem. Emphasis is placed on practical methods for applying this result to the flat, dust-filled Robertson-Walker spacetime, and the black hole interior of the Kruskal extension of the Schwarzschild spacetime.</p>