Inner horizon instability and the unstable cores of regular black holes.

We discuss the generalization of the Ori model to black holes with generic inner horizons (with arbitrary location and surface gravity), analyzing the behavior of the metric around these inner horizons under the influence of both a decaying ingoing flux of energy satisfying Price's law and an outgoing flux described by a null shell. We show that the exact solution for the late-time evolution obtained by Ori is valid for all spacetimes in which the Misner--Sharp mass is assumed to be linearly proportional to the time-dependent metric perturbations introduced. We then consider generic situations in which this linear proportionality is not assumed, obtaining asymptotic analytical expressions and performing numerical integrations that show how the exponential divergence associated with mass inflation is generically replaced at late times by a power-law divergence. We emphasize that all these geometries initially experience a first phase in which mass inflation proceeds exponentially, and describe the physical implications that follow for generic regular black holes. The formalism used also allows us to make some remarks regarding the early-time transients associated with a positive cosmological constant, known to modify the late-time behavior of ingoing perturbations from Price's law to an exponential decay. Finally we compare our analysis with that in arXiv:2010.04226v1, and illustrate specific shortcomings in the latter work that explain the differing results and, in particular, make it impossible for that analysis to recover the well-known Ori solution for Reissner--Nordstr\"om backgrounds.