Spontaneous deformation of an AdS spherical black hole

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.