On mass inflation and late-time divergences in limiting-curvature regular black holes

Abstract

Mass inflation in non-extremal regular black holes with a non-linear dependence of the Misner-Sharp mass $M$ on the asymptotic mass $m>0$ may be a transient phenomenon followed by a model-dependent non-exponential late-time divergence. We analyse these regimes based on the generalised Ori model for a class of static spherically symmetric and asymptotically flat regular black holes with a de Sitter core and an $m$-independent upper bound on the Misner-Sharp mass density and Kretschmann scalar inspired by quasi-topological gravity. We discuss the geometric mechanism behind divergences of physical quantities at the inner horizon of the perturbed spacetime, and show that these require the unphysical mass parameter inside the shell to evolve outside the positive-real domain, or in some cases force a distinct type of dynamical continuation of the static metric. Imposing an asymptotic late-time divergence in form of a fractional power-law scaling, tunable to be arbitrarily mild within the considered approximation and effectively taming mass inflation, allows us to single out a family of generalised Fan-Wang regular black holes.