Gravitational instability of an extreme Kerr black hole

TL;DR

Addresses the stability of extreme Kerr black holes under linear perturbations. The authors adapt the Aretakis horizon analysis to the Teukolsky equation and derive horizon-anchored conserved charges $I_p^{(s)}$ for perturbations of spin $s$, showing non-decay and eventual blow-up of transverse derivatives for generic data. They prove that for gravitational perturbations ( $s=±2$ ) the perturbations cannot settle to a stationary Kerr variation, indicating a linearized gravitational instability, and they extend the scalar-field instability to general extreme horizons in various dimensions via Gaussian null coordinates and a horizon-conserved quantity $I$. The results imply horizon-local instability for extreme black holes and motivate further nonlinear and quantum gravity investigations.

Abstract

Aretakis has proved the existence of an instability of a massless scalar field at the horizon of an extreme Kerr or Reissner-Nordstrom black hole: for generic initial data, a transverse derivative of the scalar field at the horizon does not decay, and higher transverse derivatives blow up. We show that a similar instability occurs for linearized gravitational, and electromagnetic, perturbations of an extreme Kerr black hole. We show also that the massless scalar field instability occurs for extreme black hole solutions of a large class of theories in various spacetime dimensions.