Abstract
In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penroseâs 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 spaceâtime 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 âgenericâ or âphysically reasonableâ spaceâtimes, 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 âAppendixâ by Erik Curiel reviews the early history of the definition of a black hole.
Highlights
Conformal diagram [146, p. 208, Fig. 37]: âThe Kruskal picture with conformal infinity represented.â Penrose usually drew his own figures in a professional, yet playful and characteristic way
Roger Penrose got half of the 2020 Physics Nobel Prize âfor the discovery that black hole formation is a robust prediction of the general theory of relativityâ
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]
Summary
Roger Penrose got half of the 2020 Physics Nobel Prize âfor the discovery that black hole formation is a robust prediction of the general theory of relativityâ. 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 LeviâCivita connection, a concept Weyl himself had co-invented) preserves their length. This makes length of vectors an absolute quantity, which a âpure infinitesimal geometryâ or a theory of general relativity should not tolerate.
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