Frozen Firewall: Generic Singularity Formation on an Extremal Horizon

TL;DR

This paper demonstrates that a broad class of nonlinear perturbations of extremal planar anti-de Sitter black holes lead to unbounded horizon curvature growth over time, with late-time behavior effectively described by linear analysis.

Contribution

It reveals that nonlinear perturbations can cause singularity formation on extremal horizons, extending understanding beyond linear perturbation results.

Findings

Nonlinear perturbations cause unbounded horizon curvature growth.

Late-time behavior is well approximated by linearized analysis.

Generic nonlinear perturbations likely lead to singularity formation.

Abstract

It is known that linearized perturbations of extremal black holes result in growing curvature on the horizon. However, nonlinear perturbations typically do not evolve to extremal black holes and do not have growing curvature at late times. We show that a large class of nonlinear perturbations of an extremal planar anti-de Sitter black hole does have horizon curvature that grows unbounded in time. The late time behavior of the nonlinear evolution is found to be captured by a linearized analysis. We argue that the generic nonlinear perturbation behaves similarly.