A critical look at singularities

The focus of the present thesis is, quite simply, spacetime singularities. We begin by providing a historical account of the idea of spacetime singularities; we look at works by Friedmann, Lemaitre, and Oppenheimer and Snyder. Next, we expose the framework introduced by Raychaudhuri, based on the notion of geodesic congruence. Then, we present the 1965 theorem by Roger Penrose and discuss some improvements suggested by the author himself in a paper where he collaborated with Hawking, this concludes the first part of the thesis where we lay down what we attempt to deconstruct in the second part. The second part opens with the discussion of the 2023 paper by Kerr, in which he contests the common interpretation of the singularity theorems. He provides examples of incomplete geodesics that do not end up at singularities, a link that seems to be taken for granted in the theorems. In the last part, we endeavour to find examples analogous to those of Kerr; investigating to that end regular metrics, the Hayward metric in particular.