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

TL;DR

This paper reviews Penrose's contributions to general relativity, focusing on singularities, black holes, and cosmic censorship, highlighting the distinctions and evolution of these concepts and their implications for the understanding of spacetime.

Contribution

It clarifies the differences between Penrose's singularity theorem, black hole definitions, and cosmic censorship conjectures, and discusses their development and significance in modern physics.

Findings

Penrose's 1965 singularity theorem does not necessarily imply black holes.

Distinction between singularities, black holes, and cosmic censorship clarified.

Evolution of cosmic censorship conjectures discussed, including PDE reformulations.

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.