Existence and nature of singularities inside black-hole horizons

Determine whether black holes described by general relativity necessarily contain spacetime singularities inside their event horizons and characterize the nature of such singularities under realistic astrophysical conditions.

Background

Black-hole interiors are central to the predictive power of general relativity and to cosmic censorship hypotheses. Although singularity theorems suggest the occurrence of singularities under broad conditions, their precise existence and physical nature inside astrophysical black holes remain subjects of debate. The authors highlight this as an explicit open question in the theoretical landscape that gravitational-wave observations indirectly inform.

References

Nevertheless, there are open questions associated to BHs, such as their stability [21-24], the existence of singularities inside their event horizon [25], and Hawking's information-loss paradox [26, 27].

— Black Hole Spectroscopy and Tests of General Relativity with GW250114  (2509.08099 - Collaboration et al., 9 Sep 2025) in Introduction

Three questions need to be answered to determine if instability arguments induce retrodiction unfriendliness:

\begin{enumerate} \item[A.] Do instability arguments apply to collapse-formed, evaporating, rotating, charged black holes? \item[B.] If so, does the instability generate spacelike or null singularities? \item[C.] If null, then are event horizons induced? \end{enumerate}

In appendix \ref{app:instability} I sketch the blue-shift arguments and discuss the status of each of these questions in the physics literature at some length. Summarising that discussion: none of the questions has an easy or known answer.

— Is Black Hole Evaporation Prediction Friendly?  (2609.09927 - Ryder, 9 Sep 2026) in Section 3, “Is Black Hole Evaporation Retrodiction Friendly?”, and Appendix, Section “Instability of Timelike Singularities”

The description of spacetime singularities remains one of the central open problems in gravitational physics.

— How much chaos can be generated by gravitational collapse before reaching the Planck scale?  (2609.11570 - Brizuela et al., 10 Sep 2026) in Section 1, Introduction