Stability of black holes in general relativity

Establish whether stationary black-hole solutions in four-dimensional vacuum general relativity—particularly the Kerr spacetime—are stable under generic gravitational perturbations at both the linear and nonlinear levels, to clarify the long-term behavior of astrophysical black holes.

Background

The paper situates its results within broader questions about black holes in general relativity. While GR has passed many experimental tests, the stability of black-hole solutions remains a foundational theoretical issue. Recent advances have resolved aspects of linear stability for Schwarzschild and made progress toward Kerr, but a complete resolution—especially nonlinear stability—has not been fully achieved. The authors explicitly list black-hole stability among the open questions motivating continued tests with gravitational waves.

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

There are some open questions for further exploration. Our construction concerns stationary, symmetry-preserving solutions. Time-dependent perturbations may produce mass inflation, while nonaxisymmetric or superradiant modes may introduce mode mixing and additional scales. It would be interesting to study whether the stationary critical layer survives as an intermediate scaling regime, or even an attractor, in the fully dynamical evolution.

— Critical Kasner scaling from Cauchy-horizon collapse near holographic phase transitions  (2609.24227 - Gao et al., 21 Sep 2026) in Section Discussion