Spontaneous Deformation of an AdS Spherical Black Hole

TL;DR

This paper explores the real-time dynamics of unstable spherical AdS black holes, revealing how axial instabilities can spontaneously deform them into axisymmetric black holes through nonlinear evolution.

Contribution

It provides the first numerical demonstration of spontaneous deformation of unstable spherical AdS black holes into axisymmetric configurations via nonlinear dynamical simulations.

Findings

Unstable spherical black holes exhibit axial instability in the spinodal region.

Imposing axial perturbations triggers nonlinear evolution leading to symmetry breaking.

Spontaneous deformation results in the formation of axisymmetric black holes.

Abstract

In this study, we investigate the real-time dynamics during the spontaneous deformation of an unstable spherical black hole in asymptotically anti-de Sitter (AdS) spacetime. For the initial value, the static solutions with spherical symmetry are obtained numerically, revealing the presence of a spinodal region in the phase diagram. From the linear stability analysis, we find that only the central part of such a thermodynamically unstable spinodal region leads to the emergence of a type of axial instability. To trigger the dynamical instability, an axial perturbation is imposed on the scalar field. As a result, by the fully nonlinear dynamical simulation, the spherical symmetry of the gravitational system is broken spontaneously, leading to the formation of an axisymmetric black hole.