Weak Cosmic Censorship Conjecture

Establish or refute the weak Cosmic Censorship Conjecture in four-dimensional asymptotically flat general relativity by proving whether generic processes (including high-angular-momentum black hole collisions and test-particle infall) can or cannot produce naked singularities visible from infinity.

Background

The notes discuss attempts to overspin or otherwise destroy black hole horizons, which would produce naked singularities and violate the Kerr bound. The weak Cosmic Censorship Conjecture asserts that such violations do not occur in physically reasonable scenarios. While perturbative analyses and numerical simulations provide supporting evidence in several settings, a general proof in four-dimensional asymptotically flat spacetimes remains elusive.

The authors review thought experiments (e.g., fine-tuned particle capture by extremal Kerr black holes) and numerical results (e.g., high-energy black hole collisions) that suggest horizons persist, yet they emphasize that the conjecture itself has not been proven in general, keeping the question open.

References

This is the subject of the weak Cosmic Censorship, that basically asserts that such a possibility does not happen. The conjecture is not proven but supported by a number of partial results, one of which is the following.

— The Physics of Black Holes and Their Environments: Consequences for Gravitational Wave Science  (2511.14841 - Cardoso et al., 18 Nov 2025) in Subsection “Testing the Cosmic Censor” (Part I: Adding rotation)

This question motivates the weak cosmic censorship conjecture according to which singularities generated by physically reasonable gravitational collapse should be hidden within black hole regions .

— Charge-Induced Pole Cancellation and Horizon Transitions in Scale-Dependent Gravitational Collapse  (2608.16341 - Muhammad et al., 17 Aug 2026) in Section 1, Introduction

Several open directions remain. First, constructing an exact rotating EMDA solution and performing the full Sorce--Wald analysis would complete the stationary case. Second, extending the variational formalism to dynamic (time-dependent) dilaton backgrounds would settle outstanding WCCC\ questions in non-stationary regimes.

— Revisit Weak Cosmic Censorship in Einstein-Maxwell-Dilaton Black Holes: Third-order Protection, Swampland Distance Conjecture, and Weak Gravity Conjectures  (2608.24557 - Lai et al., 25 Aug 2026) in Section "Conclusion and Outlook" (Section 6)

A related consistency question is whether the absorbed negative-energy or highly charged fragment can destroy the horizon.

— Electric and magnetic Penrose processes, charged-particle collisions and superradiance around a Lorentz-violating dyonic black hole  (2608.27293 - Belchior et al., 27 Aug 2026) in Introduction; Section 5, subsection “Cosmic censorship after particle absorption”; Conclusion

Penrose's Cosmic Censorship Conjecture asserts that any reasonable matter configuration collapsing under the influence of gravity will ultimately meet its fate as a black hole.

— Relativistic stellar collapse of initially static configurations  (2609.02655 - Govinder et al., 2 Sep 2026) in Section 1, Introduction