Gravitational instability of an extreme Kerr black hole

TL;DR

This paper demonstrates that extreme Kerr black holes exhibit instabilities not only for scalar fields but also for gravitational and electromagnetic perturbations, extending previous findings to more complex fields and theories.

Contribution

It extends the known scalar field instability of extreme Kerr black holes to include gravitational and electromagnetic perturbations across various theories and dimensions.

Findings

Instability occurs for gravitational and electromagnetic perturbations.

Scalar field instability extends to a broad class of theories and dimensions.

Higher derivatives of perturbations blow up at the horizon.

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.