Quantum fluxes at the inner horizon of a spinning black hole

TL;DR

This paper investigates how quantum effects influence the inner horizon of evaporating rotating black holes, revealing that quantum fluxes generally diverge and can alter the horizon's stability.

Contribution

It provides the first conclusive demonstration that quantum fluxes diverge at the Cauchy horizon of four-dimensional spinning black holes, considering backreaction effects.

Findings

Quantum flux components are generally non-zero at the Cauchy horizon.

Flux components change sign depending on black hole spin and polar angle.

Fluxes diverge on the Cauchy horizon, indicating irregularity under semiclassical effects.

Abstract

Rotating or charged classical black holes in isolation possess a special surface in their interior, the Cauchy horizon, beyond which the evolution of spacetime (based on the equations of General Relativity) ceases to be deterministic. In this work, we study the effect of a quantum massless scalar field on the Cauchy horizon inside a rotating (Kerr) black hole that is evaporating via the emission of Hawking radiation (corresponding to the field being in the Unruh state). We calculate the flux components (in Eddington coordinates) of the renormalized stress-energy tensor of the field on the Cauchy horizon, as functions of the black hole spin and of the polar angle. We find that these flux components are generically non-vanishing. Furthermore, we find that the flux components change sign as these parameters vary. The signs of the fluxes are important, as they provide an indication of whether the Cauchy horizon expands or crushes (when backreaction is taken into account). Regardless of these signs, our results imply that the flux components generically diverge on the Cauchy horizon when expressed in coordinates which are regular there. This is the first time that irregularity of the Cauchy horizon under a semiclassical effect is conclusively shown for (four-dimensional) spinning black holes.