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.
