Horizon Instability of Extremal Black Holes

TL;DR

This paper demonstrates that extremal black hole horizons are linearly unstable under scalar perturbations, with derivatives not decaying and higher derivatives diverging over time, unlike subextremal black holes.

Contribution

It establishes the linear instability of extremal horizons under scalar perturbations, highlighting a stark contrast with subextremal cases.

Findings

Derivatives of solutions do not decay along extremal horizons.

Higher order derivatives blow up over time.

Instability applies to extremal Kerr-Newman and Majumdar-Papapetrou spacetimes.

Abstract

We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This result holds in particular for extremal Kerr-Newman and Majumdar-Papapetrou spacetimes and is in stark contrast with the subextremal case for which decay is known for all derivatives along the event horizon.