Nonlinear instability of scalar fields on extremal black holes

TL;DR

This paper demonstrates a novel finite-time blow-up phenomenon for certain wave equations on extremal black holes, with singularities forming at the event horizon even from near-trivial initial data, unlike in non-extremal cases.

Contribution

It establishes a new type of nonlinear instability specific to extremal black holes, showing finite-time blow-up at the horizon from arbitrarily small initial perturbations.

Findings

Finite-time blow-up occurs along the event horizon.

No similar instability for subextremal black holes or Minkowski space.

Initial data can be arbitrarily close to trivial.

Abstract

We prove a new type of finite time blow-up for a class of semilinear wave equations on extremal black holes. The initial data can be taken to be arbitrarily close to the trivial data. The first singularity occurs along the (degenerate) future event horizon. No analogue of this instability occurs for subextremal black holes or the Minkowski spacetime.