Math 2.0

Relativity and gravitational theory Black holes Conjecture

Weak cosmic censorship conjecture

Builds on Asymptotically flat spacetimeGlobally hyperbolic spacetimeChoquet-Bruhat–Geroch theorem on maximal developmentsEvent horizonGravitational singularity

Statement

Consider the vacuum Einstein field equations, or the Einstein equations coupled to a suitable matter model. Let the initial data be asymptotically flat, complete and generic. Then the maximal globally hyperbolic development of the data, given by the Choquet-Bruhat–Geroch theorem, has a complete future null infinity.

Remarks

Informally, singularities formed by gravitational collapse are hidden from distant observers inside an event horizon: there are no naked singularities. The formulation with complete future null infinity is due to Christodoulou; Penrose's original 1969 statement was not given in precise mathematical form. The word "generic" cannot be dropped. Christodoulou constructed spherically symmetric solutions of the Einstein equations coupled to a scalar field in which a naked singularity forms. He later proved that such solutions are unstable under perturbation of the data. The conjecture is open in general. It is a hypothesis behind several classical results, such as the Hawking area theorem.

Reading path

To understand this page from the ground up, read these 28 pages in order. The foundations come first.

Show the path as a graph
Asymptotically flat spacetime, concept, no evidence levelAsymptotically flat s…conceptCauchy surface, concept, no evidence levelCauchy surfaceconceptEuclidean space, object, no evidence levelEuclidean spaceobjectEvent horizon, concept, no evidence levelEvent horizonconceptFunction, concept, no evidence levelFunctionconceptFunction composition, concept, no evidence levelFunction compositionconceptGlobally hyperbolic spacetime, concept, no evidence levelGlobally hyperbolic s…conceptGravitational singularity, concept, no evidence levelGravitational singula…conceptHarmonic coordinate condition, concept, no evidence levelHarmonic coordinate c…conceptInitial value formulation of general relativity, concept, no evidence levelInitial value formula…conceptFréchet derivative, definition, no evidence levelFréchet derivativedefinitionFunction of several variables, concept, no evidence levelFunction of several v…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptLimit of a function of several variables, concept, no evidence levelLimit of a function o…conceptPartial derivative, definition, no evidence levelPartial derivativedefinitionDifferentiable function of several variables, definition, no evidence levelDifferentiable functi…definitionHigher partial derivatives, definition, no evidence levelHigher partial deriva…definitionJacobian matrix, definition, no evidence levelJacobian matrixdefinitionDifferentiable on an open set, definition, no evidence levelDifferentiable on an …definitionChain rule in several variables, statement, no evidence levelChain rule in several…statementIterated derivative, definition, no evidence levelIterated derivativedefinitionJacobian determinant, definition, no evidence levelJacobian determinantdefinitionDerivative of the inverse function, statement, no evidence levelDerivative of the inv…statementC^k function characterised by continuous derivatives, statement, no evidence levelC^k function characte…statementInverse function theorem, statement, no evidence levelInverse function theo…statementDiffeomorphism, definition, no evidence levelDiffeomorphismdefinitionChoquet-Bruhat–Geroch theorem on maximal developments, statement, no evidence levelChoquet-Bruhat–Geroch…statementWeak cosmic censorship conjecture, conjecture, no evidence levelWeak cosmic censorshi…conjecture
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Asymptotically flat spacetime concept
  2. Cauchy surface concept
  3. Euclidean space object
  4. Event horizon concept
  5. Function concept
  6. Function composition concept
  7. Globally hyperbolic spacetime concept
  8. Gravitational singularity concept
  9. Harmonic coordinate condition concept
  10. Initial value formulation of general relativity concept
  11. Fréchet derivative definition
  12. Function of several variables concept
  13. Partial derivative concept
  14. Limit of a function of several variables concept
  15. Partial derivative definition
  16. Differentiable function of several variables definition
  17. Higher partial derivatives definition
  18. Jacobian matrix definition
  19. Differentiable on an open set definition
  20. Chain rule in several variables statement
  21. Iterated derivative definition
  22. Jacobian determinant definition
  23. Derivative of the inverse function statement
  24. C^k function characterised by continuous derivatives statement
  25. Inverse function theorem statement
  26. Diffeomorphism definition
  27. Choquet-Bruhat–Geroch theorem on maximal developments statement
  28. Weak cosmic censorship conjecture conjecture

Further reading

  1. Web https://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis
About this page
TagCJYVF1RED6
URIm2://CJYVF1RED6
Kindconjecture
WritingW0 stub
MSC83C75, 83C57, 83C05
StatusThis copy of the site has no build data. Run m2 status CJYVF1RED6.
AboutGravitational singularity, Black hole
UsesAsymptotically flat spacetime, Globally hyperbolic spacetime, Choquet-Bruhat–Geroch theorem on maximal developments, Event horizon, Gravitational singularity
Changed3 November 2026

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