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.

arXiv comment30 pages, 1 figure. v2 was thorough revision; v3 benefited from a discussion with Penrose; v4 adds missing references and small clarifications

References in corpus (22)

• Stationary Black Holes: Uniqueness and Beyond
• Notes on non-singular models of black holes
• Critical phenomena in gravitational collapse
• Singularity Theorems and Their Consequences
• The 1965 Penrose singularity theorem
• Geodesically complete black holes
• Black holes without spacelike singularities
• Present status of the Penrose inequality
• Violating weak cosmic censorship in AdS${}_4$
• The Many Definitions of a Black Hole
• Strong cosmic censorship: taking the rough with the smooth
• Causal structures and causal boundaries
• On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornification
• Spacetime Singularities and Cosmic Censorship Conjecture: A Review with Some Thoughts
• Regular black holes from semi-classical down to Planckian size
• The causal boundary of wave-type spacetimes
• Globally hyperbolic spacetimes can be defined without the 'causal' condition
• Determinism and general relativity
• Singularities, black holes, and cosmic censorship: A tribute to Roger Penrose
• The interior of dynamical extremal black holes in spherical symmetry
• Gravitation and General Relativity at King's College London
• The eye of the storm: A regular Kerr black hole

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• 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