Singularity Theorems and Their Consequences

TL;DR

This paper reviews the history, hypotheses, and implications of singularity theorems in general relativity, clarifying misconceptions and analyzing their consequences with examples, after correcting publication errors affecting citations.

Contribution

It provides a comprehensive, corrected review of singularity theorems, discussing their hypotheses, implications, and common misconceptions with detailed examples.

Findings

Clarifies the hypotheses of singularity theorems

Analyzes the implications and consequences of singularity theorems

Provides corrected and clarified references for future citations

Abstract

This is a 20-year old review on singularities and singularity theorems. The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains wrong headers and footers in its 1st page. This has led to many wrong citations, and to some confusion. The pdf file here contains the right information. ORIGINAL ABSTRACT: A detailed study of the singularity theorems is presented. I discuss the plausibility and reasonability of their hypotheses, the applicability and implications of the theorems, as well as the theorems themselves. The consequences usually extracted from them, some of them without the necessary rigour, are widely and carefully analysed with many clarifying examples and alternative views.