Uma análise do teorema de singularidade de penrose sob a ação de transformações disformes

Abstract

In this dissertation, after a brief review of the elements present in differential geometry, we present Penrose’s Singularity Theorem (1965) and rewrite it from the perspective of disformal transformations. Without intending to use a complete and sophisticated mathematical apparatus, we are going to present an outline of the proof of the Singularity Theorem and a brief alternative to it. Then, separating the disformal transformations into two complementary classes, more specifically the conformal case and the Kerr-Schild type transformations, we will present an analysis of the Singularity Theorem according to these transformations. Finally, we were able to make an analysis of space-times that relate through the disformal transformations and thus describe the hypotheses necessary for the addition or removal of singularities.