Penrose singularity theorem

E1018070

result in mathematical physics singularity theorem theorem in general relativity

The Penrose singularity theorem is a fundamental result in general relativity showing that, under physically reasonable conditions such as gravitational collapse, spacetime must contain singularities where classical physics breaks down.

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Label	Occurrences
Penrose singularity theorem canonical	1

Statements (47)

Predicate	Object
instanceOf	result in mathematical physics ⓘ singularity theorem ⓘ theorem in general relativity ⓘ
appliesTo	Lorentzian manifolds NERFINISHED ⓘ spacetimes satisfying Einstein field equations ⓘ
assumes	classical general relativity is valid ⓘ existence of a closed trapped surface ⓘ existence of a non-compact Cauchy surface or appropriate causality conditions ⓘ global hyperbolicity is violated by trapped surface formation ⓘ null energy condition ⓘ
author	Roger Penrose NERFINISHED ⓘ
concludes	breakdown of classical spacetime description ⓘ existence of singularities in spacetime ⓘ spacetime is null geodesically incomplete ⓘ
countryOfOrigin	United Kingdom ⓘ
describedAs	first rigorous proof of generic singularity formation in gravitational collapse ⓘ
field	differential geometry ⓘ general relativity NERFINISHED ⓘ gravitational physics ⓘ mathematical relativity ⓘ
implies	black hole formation leads to geodesic incompleteness ⓘ singularities form in gravitational collapse under generic conditions ⓘ
influenced	development of modern black hole theory ⓘ research on quantum gravity ⓘ study of global properties of spacetime ⓘ
language	English ⓘ
motivationFor	cosmic censorship hypothesis NERFINISHED ⓘ
namedAfter	Roger Penrose NERFINISHED ⓘ
originalTitle	Gravitational Collapse and Space-Time Singularities NERFINISHED ⓘ
publishedIn	Physical Review Letters NERFINISHED ⓘ
relatedTo	Hawking singularity theorem NERFINISHED ⓘ Hawking–Penrose singularity theorems NERFINISHED ⓘ black hole physics ⓘ cosmic censorship conjecture NERFINISHED ⓘ gravitational collapse ⓘ
requires	Einstein field equations with reasonable matter content ⓘ smooth spacetime manifold ⓘ
status	widely accepted in classical general relativity ⓘ
topic	causal structure ⓘ geodesic incompleteness ⓘ spacetime singularities ⓘ
usesConcept	Raychaudhuri equation NERFINISHED ⓘ causal structure of spacetime ⓘ global techniques in Lorentzian geometry ⓘ null geodesic congruence ⓘ trapped surface ⓘ
yearProved	1965 ⓘ

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Full triples — surface form annotated when it differs from this entity's canonical label.

Hawking–Penrose singularity theorems → hasPart → Penrose singularity theorem ⓘ