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

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.

30 pages, 1 figure. v2 was thorough revision; v3 benefited from a discussion with Penrose; v4 adds missing references and small clarifications

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• Notes on non-singular models of black holes
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• The 1965 Penrose singularity theorem
• Present status of the Penrose inequality
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• Black Hole singularity and its possible mitigations: Reformulation of Penrose Singularity theorem using null Raychaudhuri matrix
• Unveiling horizons in quantum critical collapse
• Gravitational collapse of a spherical scalar field
• Dynamical hair growth in black hole binaries in Einstein-scalar-Gauss-Bonnet gravity
• A note on Strong Cosmic Censorship and its violation in Reissner-Nordström de Sitter black hole space-times
• Radial Gravitational Collapse Causes Timelike Incompleteness
• Primordial Black Holes: A Review of Formation and Evolution