Omkar Deshpande, BS (Hons), Class of 2023

Supervisor: Professor Gaurav Goswami, School of Arts and Sciences

Thesis Brief

One of the most peculiar features of gravity that Newtonian mechanics failed to formulate are black holes and the spacetime singularities. The general theory of relativity could formalise it precisely due to its reliance on the rigorously established differential geometry as well as algebraic topology. This shift of paradigm and its further formalism by Hawking and Penrose has given rise to a whole set of new problems pertaining to singularities. The most relevant of all being the cosmic censorship conjecture, which is an attempt to propose that every singularity has some sort of trapped region that causally censors it. This thesis aims to precisely state the underlying formalism for singularity theorems and trapped surfaces to motivate these concepts with mathematical rigour. This is done by firstly developing a definition for spacetime along with the proof for the infamous Einstein field equations. What follows are the phenomenological conditions: Energy conditions and Causality conditions for one to move from an abstract spacetime to physically relevant ones. In the latter parts of the thesis, an abstract description of trapped surfaces and their relevance to singularity theorem is given in the context of the cosmic censorship conjecture. Furthermore, two physically relevant case studies: Datt-Oppenheimer-Snyder and Joshi-Malafarina-Narayan spacetimes are given attention as examples pertaining to the conjecture. Finally, the thesis also briefly explains the future scope of research that can be carried out.