What happens at the horizon(s) of an extreme black hole?

TL;DR

This paper investigates the nonlinear evolution of scalar field instabilities at the horizon of extreme black holes, revealing that most evolve to non-extreme states, but fine-tuned conditions can produce dynamic extreme black holes with unique horizon properties.

Contribution

It provides the first numerical analysis of nonlinear scalar field instabilities on extreme black holes, showing the potential for dynamic extreme black holes with smooth horizons and C^1 extensions.

Findings

Most perturbations lead to non-extreme Reissner-Nordstrom black holes.

Fine-tuned initial conditions can produce time-dependent extreme black holes.

The event horizon remains smooth, but late-time observers see large gradients.

Abstract

A massless scalar field exhibits an instability at the event horizon of an extreme black hole. We study numerically the nonlinear evolution of this instability for spherically symmetric perturbations of an extreme Reissner-Nordstrom (RN) black hole. We find that generically the endpoint of the instability is a non-extreme RN solution. However, there exist fine-tuned initial perturbations for which the instability never decays. In this case, the perturbed spacetime describes a time-dependent extreme black hole. Such solutions settle down to extreme RN outside, but not on, the event horizon. The event horizon remains smooth but certain observers who cross it at late time experience large gradients there. Our results indicate that these dynamical extreme black holes admit a C^1 extension across an inner (Cauchy) horizon.