Penrose's 1965 singularity theorem: From geodesic incompleteness to cosmic censorship

TL;DR

This paper provides a detailed historical and conceptual analysis of Penrose's 1965 singularity theorem, highlighting its assumptions, limitations, and the connection to cosmic censorship conjectures, emphasizing that the theorem alone does not prove black hole formation.

Contribution

It offers a nuanced understanding of the assumptions behind Penrose's theorem and clarifies its relation to cosmic censorship and black hole formation.

Findings

The theorem relies on assumptions that do not guarantee black hole existence.

Penrose was aware of the theorem's limitations and proposed cosmic censorship to address them.

The theorem's actual content differs from its physical goals.

Abstract

Supplementing earlier literature by e.g. Tipler, Clarke, & Ellis (1980), Israel (1987), Thorne, (1994), Earman (1999), Senovilla & Garfinkle (2015), Curiel (2019ab), and Landsman (2021ab), I provide a historical and conceptual analysis of Penrose's path-breaking 1965 singularity (or incompleteness) theorem. The emphasis is on the nature and historical origin of the assumptions and definitions used in-or otherwise relevant to-the theorem, as well as on the discrepancy between the (astro)physical goals of the theorem and its actual content: even if its assumptions are met, the theorem fails to prove the existence or formation of black holes.Penrose himself was well aware of this gap, which he subsequently tried to overcome with his visionary and influential cosmic censorship conjectures. Roughly speaking, to infer from (null) geodesic incompleteness that there is a "black" object one needs weak cosmic censorship, whereas in addition a "hole" exists (as opposed to a boundary of an extendible space-time causing the incompleteness of geodesics) if strong cosmic censorship holds.