Stability of the Cauchy horizon in Kerr--de Sitter spacetimes

TL;DR

This paper investigates the stability of the Cauchy horizon inside rotating black holes with a positive cosmological constant, showing conditions under which wave energy fluxes remain finite, allowing potential passage through the horizon.

Contribution

It generalizes Teukolsky's equation for Kerr--de Sitter spacetimes and analyzes wave flux regularity at the Cauchy horizon, revealing critical stability conditions.

Findings

Energy fluxes are regular at the Cauchy horizon under specific surface gravity conditions.

The stability condition is narrowly satisfied even with small cosmological constants.

Potential for observers to pass through the horizon viewing the naked singularity.

Abstract

We begin a program of work aimed at examining the interior of a rotating black hole with a non--zero cosmological constant. The generalisation of Teukolsky's equation for the radial mode functions is presented. It is shown that the energy fluxes of scalar, electromagnetic and gravity waves are regular at the Cauchy horizon whenever the surface gravity there is less than the surface gravity at the cosmological horizon. This condition is narrowly allowed, even when the cosmological constant is very small, thus permitting an observer to pass through the hole, viewing the naked singularity along the way.