Math 2.0

Relativity and gravitational theory Black holes Conjecture

Strong cosmic censorship conjecture

Builds on Globally hyperbolic spacetimeChoquet-Bruhat–Geroch theorem on maximal developmentsGravitational singularity

Statement

Consider the vacuum Einstein field equations, or the Einstein equations coupled to a suitable matter model. Let the initial data be generic, either asymptotically flat or given on a compact manifold. Then the maximal globally hyperbolic development of the data, given by the Choquet-Bruhat–Geroch theorem, is inextendible as a suitably regular Lorentzian manifold.

Remarks

The statement says that classical general relativity is deterministic for generic data: the data fix the whole spacetime. No observer can cross a Cauchy horizon into a region the data do not determine. The answer depends on the regularity class allowed for the extension. The Kerr and Reissner–Nordström black holes are not generic: their maximal developments extend smoothly across an inner Cauchy horizon, beyond which the singularity is visible. In 2017 Dafermos and Luk showed that, assuming the stability of the Kerr exterior, the Kerr Cauchy horizon is stable in the class of continuous metrics. So the version with continuous extensions is false. Versions with stronger regularity, such as Christodoulou's formulation with locally square-integrable Christoffel symbols, remain open. Despite their names, the strong and weak cosmic censorship conjectures do not imply each other.

Reading path

To understand this page from the ground up, read these 26 pages in order. The foundations come first.

Show the path as a graph
Cauchy surface, concept, no evidence levelCauchy surfaceconceptEuclidean space, object, no evidence levelEuclidean spaceobjectFunction, 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…conceptLimit of a function of several variables, concept, no evidence levelLimit of a function o…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptDifferentiable function of several variables, definition, no evidence levelDifferentiable functi…definitionPartial derivative, definition, no evidence levelPartial derivativedefinitionDifferentiable on an open set, definition, no evidence levelDifferentiable on an …definitionJacobian matrix, definition, no evidence levelJacobian matrixdefinitionChain rule in several variables, statement, no evidence levelChain rule in several…statementHigher partial derivatives, definition, no evidence levelHigher partial deriva…definitionIterated 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…statementStrong cosmic censorship conjecture, conjecture, no evidence levelStrong cosmic censors…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. Cauchy surface concept
  2. Euclidean space object
  3. Function concept
  4. Function composition concept
  5. Globally hyperbolic spacetime concept
  6. Gravitational singularity concept
  7. Harmonic coordinate condition concept
  8. Initial value formulation of general relativity concept
  9. Fréchet derivative definition
  10. Function of several variables concept
  11. Limit of a function of several variables concept
  12. Partial derivative concept
  13. Differentiable function of several variables definition
  14. Partial derivative definition
  15. Differentiable on an open set definition
  16. Jacobian matrix definition
  17. Chain rule in several variables statement
  18. Higher partial derivatives definition
  19. Iterated derivative definition
  20. Jacobian determinant definition
  21. Derivative of the inverse function statement
  22. C^k function characterised by continuous derivatives statement
  23. Inverse function theorem statement
  24. Diffeomorphism definition
  25. Choquet-Bruhat–Geroch theorem on maximal developments statement
  26. Strong cosmic censorship conjecture conjecture

Further reading

  1. Web https://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis
About this page
TagC663A9H5DM
URIm2://C663A9H5DM
Kindconjecture
WritingW0 stub
MSC83C75, 83C05
StatusThis copy of the site has no build data. Run m2 status C663A9H5DM.
AboutGravitational singularity
UsesGlobally hyperbolic spacetime, Choquet-Bruhat–Geroch theorem on maximal developments, Gravitational singularity
Changed3 November 2026

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