Frozen Firewall: Generic Singularity Formation on an Extremal Horizon

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.