A critical appraisal of the singularity theorems

TL;DR

This paper critically examines the singularity theorems, especially Penrose's, clarifying misconceptions, analyzing their hypotheses, implications, and the nature of black hole singularities, in light of recent renewed interest due to the Nobel Prize.

Contribution

It provides a comprehensive critique of the singularity theorems, discussing their assumptions, consequences, and the role of spacetime extensions, which is rarely addressed in detail.

Findings

Clarifies misconceptions about the theorems

Analyzes the implications for black hole singularities

Discusses spacetime extensions in relation to the theorems

Abstract

The 2020 Nobel prize in Physics has revived the interest in the singularity theorems and, in particular, in the Penrose theorem published in 1965. In this short paper I briefly review the main ideas behind the theorems and then proceed to an evaluation of their hypotheses and implications. I will try to dispel some common misconceptions about the theorems and their conclusions, as well as to convey some of their rarely mentioned consequences. In particular, a discussion of spacetime extensions in relation to the theorems is provided. The nature of the singularity inside black holes is also analyzed.