Singularities, black holes, and cosmic censorship: A tribute to Roger Penrose

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.

28 pages. Section 3.2 expanded by a page and some references added

References in corpus (5)

• The 1965 Penrose singularity theorem
• Testing the black hole "no-hair" hypothesis
• Less is Different: Emergence and Reduction Reconciled
• Spacetime Singularities and Cosmic Censorship Conjecture: A Review with Some Thoughts
• Characteristic initial data and smoothness of Scri. II. Asymptotic expansions and construction of conformally smooth data sets

Cited by in corpus (9)

• Primordial black hole constraints with Hawking radiation -- a review
• Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
• Penrose's 1965 singularity theorem: From geodesic incompleteness to cosmic censorship
• A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
• The singularity theorems of General Relativity and their low regularity extensions
• Semiclassical black holes and horizon singularities
• Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes
• Black holes and their horizons in semiclassical and modified theories of gravity
• The no-hair theorems at work in the tidal disruption event AT2020afhd