Regular evaporating black holes with stable cores
A. Bonanno, Amir-Pouyan Khosravi, Frank Saueressig
Abstract
A feature shared by many regular black hole spacetimes is the occurrence of a Cauchy horizon. It is then commonly believed that this renders the geometry unstable against perturbations through the mass-inflation effect. In this work, we perform the first dynamical study of this effect taking into account the mass-loss of the black hole due to Hawking radiation. It is shown that the time-dependence of the background leads to two novel types of late-time behavior whose properties are entirely determined by the Hawking flux. The first class of attractor-behavior is operative for regular black holes of the Hayward and renormalization group improved type and characterized by the square of the Weyl curvature growing as ${v}^{6}$ at asymptotically late times. This singularity is inaccessible to a radially free-falling observer though. The second class is realized by Reissner-Nordstr\"om black holes and regular black holes of the Bardeen type. In this case the curvature scalars remain finite as $v\ensuremath{\rightarrow}\ensuremath{\infty}$. Thus the Hawking flux has a profound effect on the mass-inflation instability, either weakening the effect significantly or even expelling it entirely.