Penrose’s 1965 singularity theorem: from geodesic incompleteness to cosmic censorship

Supplementing earlier literature by e.g. Tipler et al. (1980), Israel (1987), Thorne (1994), Earman (1999), Senovilla and Garfinkle (2015), Curiel (2019) and Landsman (2021), 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.