Geometry near the inner horizon of a rotating, accreting black hole

Abstract

Here we present a novel classical model to describe the near-inner horizon geometry of a rotating, accreting black hole. The model assumes spacetime is homogeneous and is sourced by radial streams of a collisionless, null fluid, and it predicts that the standard Poisson-Israel mass inflation phenomenon will be interrupted by a Kasner-like collapse toward a spacelike singularity. Thus, the inner horizon and any additional structure beyond it never gets a chance to form. Such a model is shown to be valid near the inner horizon of astrophysically realistic black holes through comparison to the conformally separable Kerr model, which provides a natural connection of the Kerr metric to a self-similar, accreting spacetime. We then analyze the behavior of null geodesics in our model, connecting them to the Kerr metric in order to answer the practical question of what an infalling observer approaching the inner horizon might see. We find that an infalling zero-energy observer near the inner horizon will initially see streams of matter accelerating at high energies along the radial direction. Then, within a short span of proper time, the geometry will enter a collapse phase as most of the background sky becomes squashed along the edge of the black hole's shadow. Classically, the observer's journey will end here at a spacelike singularity, though the final outcome of the collapse will require a future calculation of the quantum back reaction within this framework.