John Chunko with Tanmay Vachaspati

Singularities in General Relativity

The determination of the presence of singularities in a general spacetime can be a very difficult task, especially since many apparent singularities can be removed by an appropriate coordinate transformation on the spacetime. One is therefore led to the construction of a set of rules that allow one to determine if non-coordinate singularities, namely, curvature singularities, are present in the spacetime under consideration.  Such sets of rules are known as singularity theorems. These singularity theorems allow one to determine if actual singularities are present in a general spacetime if that spacetime satisfies certain energy and causal conditions.

The goals of this project will therefore be to study how these singularity theorems are constructed, as well as to apply them to specific spacetimes. To accomplish this goal we will have to examine how both timelike and null geodesics behave in curved spacetimes with specific requirements placed upon the curvature-inducing stress-energy tensor. We will then introduce the concept of causal structure and examine how this structure influences our previous results. We will then be able to formulate the singularity theorems for general spacetimes. Applications of these theorems to specific spacetimes will then be attempted.