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Weak cosmic censorship conjecture

About 23 years old · traced to

Let asymptotically flat initial data for Einstein's field equations be given, and let its maximal development be the corresponding spacetime. A future null infinity I+\mathcal{I}^+ is complete if it is complete as a null hypersurface; a singularity is hidden from I+\mathcal{I}^+ when it lies in a black-hole region causally disconnected from I+\mathcal{I}^+. Weak cosmic censorship conjecture. For generic asymptotically flat initial data, the maximal development of Einstein's field equations possesses a complete future null infinity I+\mathcal{I}^+ and hides the possibly formed singularities in a black-hole region causally disconnected from I+\mathcal{I}^+. This is one of the greatest open problems in classical general relativity and concerns whether singularities arising from generic gravitational data can be observed from infinity.

References

Primary source

Xinliang An, “Naked Singularity Censoring with Anisotropic Apparent Horizon”, arXiv:2401.02003 (2024).

Additional references

5 papers in this index state this conjecture (2003–2024). The statement above is taken from the most recent of them; the others are arXiv:2210.11325, arXiv:1909.07345, arXiv:1107.0949, arXiv:gr-qc/0309115.

cosmic-censorshipgeneral-relativitysingularities
Posted

Progress summary

Refreshed
Claimed progress

A new perturbative study claims extra protection against naked singularities in one black-hole model, but the general conjecture remains open.

Proposed by Roger Penrose in 1969, the conjecture says that singularities formed from generic isolated gravitational data remain hidden from distant observers. The full claim for generic asymptotically flat data has neither a general proof nor a decisive disproof.

Known results

  • Penrose (1965): small perturbations of Schwarzschild data still produce geodesically incomplete developments, establishing singularity formation but not censorship.
  • Choptuik (1993): spherical scalar collapse yields a finely tuned naked singularity, hence a nongeneric example.
  • Christodoulou (1990s): naked-singularity data exist, but arbitrarily small perturbations produce black holes, supporting nongenericity.
  • Crisford and Santos (2017): a four-dimensional anti-de Sitter counterexample lies outside the asymptotically flat conjecture.

August 2026 third-order protection claim

A preprint posted in August 2026 claims that third-order perturbation analysis prevents overcharging, and thus horizon destruction, for a static charged GMG Einstein-Maxwell-dilaton black hole. This is a perturbative special-case result, not a proof of generic weak cosmic censorship.

Current status (as of August 2026): Special-case protections and nongeneric or non-asymptotically-flat counterexamples are known, but the generic asymptotically flat conjecture remains open; the August 2026 third-order claim is unverified.

Sources

Solutions 0

No solutions have been posted yet.