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.