A new study has resolved the global nonlinear stability problem for the family of Kerr black holes across the full subextremal range. Spacetimes evolving from initial data close to those of a subextremal Kerr black hole, as solutions of the Einstein vacuum equation Ric(g)=0, settle down to a nearby member of the Kerr family at a decay rate of O(t*^(-2-εK)) in spatially compact regions. This breakthrough addresses a fundamental question regarding the persistence of these solutions in general relativity.

To achieve this demonstration, the researchers utilized a generalized wave map gauge, modified using gauge source terms that lie in a suitable finite-dimensional space determined by the expansion of the initial data. Unlike previous work that often relied on reductions to scalar equations, this study works directly with the tensorial equation. The final black hole parameters (mass and angular momentum), the gravitational wave tail, and the gauge source terms were treated as unknowns within a nonlinear Nash-Moser iteration scheme.

The work builds upon two companion papers by the same author. The first introduces a strong form of constraint damping in the full subextremal range, which is used in the formulation of the gauge-fixed Einstein equation. The second provides tame estimates for forward solutions of a general class of wave-type equations, which include the linearizations of the gauge-fixed Einstein equation arising in the nonlinear iteration scheme. These estimates are crucial for the study's detailed asymptotic analysis.

The confirmation of the nonlinear stability of subextremal Kerr black holes is a significant milestone in understanding general relativity and the evolution of the most extreme astrophysical objects. It implies that, under realistic perturbations, these black holes tend to return to an equilibrium state described by the Kerr metric, reinforcing their role as stable and physically relevant solutions to Einstein's equations.