Abstract

In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space–time does not match the generally accepted definition of a black hole (derived from his concept of null infinity). To overcome this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the pde literature. As a compromise, one might say that in “generic” or “physically reasonable” space–times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an “Appendix” by Erik Curiel reviews the early history of the definition of a black hole.

Highlights

  • Conformal diagram [146, p. 208, Fig. 37]: ‘The Kruskal picture with conformal infinity represented.’ Penrose usually drew his own figures in a professional, yet playful and characteristic way

  • Roger Penrose got half of the 2020 Physics Nobel Prize ‘for the discovery that black hole formation is a robust prediction of the general theory of relativity’

  • In Penrose [142,143,144,145,146, 148] he introduced most of the global causal techniques and topological ideas that are central to any serious mathematical analysis of both gr and Lorentzian geometry [135, 139]

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Summary

Historical Introduction

Roger Penrose got half of the 2020 Physics Nobel Prize ‘for the discovery that black hole formation is a robust prediction of the general theory of relativity’. Page 3 of 38 42 surfaces, his real argument for conformal invariance was that what he calls Reine Infinitesimalgeometrie must go beyond Riemannian geometry, which (so he thinks) suffers from the inconsistency that parallel transport of vectors (through the metric or Levi–Civita connection, a concept Weyl himself had co-invented) preserves their length. This makes length of vectors an absolute quantity, which a ‘pure infinitesimal geometry’ or a theory of general relativity should not tolerate.

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Definitions
Null Infinity
17 If R g
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Trapped Surfaces
Singularities in Space–Time
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Cosmic Censorship
Cosmic Censorship Ă  la Penrose
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Examples
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Epilogue
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Full Text
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