Linear stability of Kerr black holes in the full subextremal range

TL;DR

This paper proves the unconditional linear stability of Kerr black holes across the entire subextremal range, extending previous results to the full parameter space using advanced mode stability and zero energy analysis techniques.

Contribution

It establishes the full subextremal linear stability of Kerr black holes, building on prior slow-rotation results and incorporating new mode stability and zero energy behavior analyses.

Findings

Proves linear stability for all subextremal Kerr black holes.

Utilizes mode stability results by Andersson, Whiting, and others.

Analyzes zero energy behavior of the linearized Einstein equations.

Abstract

We prove, unconditionally, the linear stability of the Kerr family in the full subextremal range. On an analytic level, our proof is the same as that of our earlier paper in the slowly rotating case. The additional ingredients we use are, firstly, the mode stability result proved by Andersson, Whiting, and the first author and, secondly, computations related to the zero energy behavior of the linearized gauge-fixed Einstein equation in work by the second author.