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Joined 2026-09-21 Message
Incoming links: Roger Penrose
Nobel Prize in Physics in 2020 2026-10-18
One half went to Roger Penrose for showing that black hole formation is a robust prediction of general relativity. One quarter each went to Reinhard Genzel and Andrea Ghez for discovering a supermassive compact object at the centre of the Milky Way.[ref]
The Nobel Prize in Physics 2020 by Nobel Prize Outreach. Individual official summary: Penrose one half for robust relativistic black-hole formation; Genzel and Ghez one quarter each for the Galactic-centre compact object.
Penrose singularity theorem Created 2026-09-24 Updated 2026-10-18
The Penrose singularity theorem states that a globally hyperbolic spacetime with a noncompact Cauchy hypersurface, a closed trapped surface, and the null convergence condition is future null-geodesically incomplete. Time reversal replaces the trapped surface by an anti-trapped surface and gives past incompleteness.
In his 1965 paper Gravitational Collapse and Space-Time Singularities, Roger Penrose used trapped surfaces and global causal structure to address whether nonspherical perturbations could avert a breakdown during gravitational collapse. Quasars supplied the opening astrophysical motivation. The paper used metric signature and a stronger timelike local-energy assumption; the statement above uses the modern null convergence condition.[ref]
Gravitational Collapse and Space-Time Singularities by Roger Penrose. pp. 57–58, motivation and trapping
For this version, take a smooth connected four-dimensional spacetime with a time orientation. A Cauchy hypersurface meets every inextendible causal curve exactly once; its existence expresses global hyperbolicity. The hypersurface must be noncompact, meaning not compact; this is a global spatial condition, not an assumption about the size of the collapsing body. The null convergence condition is for every null vector . Through the Einstein field equations it follows from the null energy condition; a cosmological constant drops out of the null contraction.[ref]
The conclusion is that at least one future-inextendible null geodesic has a finite upper endpoint of its affine parameter. It neither asserts infinite mass density or divergent curvature at every endpoint, nor says that such an endpoint is visible. Locating an event horizon requires additional global information; the theorem is not a horizon-finding rule for arbitrary spacetimes. Weak cosmic censorship conjecture is an additional issue.[ref]
The 1965 Penrose singularity theorem by José M. Martín Senovilla and David Garfinkle. section 4.1, printed pp. 11–12; section 6.1, cosmic censorship
The supermassive black hole account describes the motivating observational evidence from stellar orbits at the Galactic centre. Such measurements infer a compact gravitating mass. They do not observe a trapped surface, measure a geodesic's complete future, or experimentally prove the Penrose singularity theorem.