Singularities in rotating black holes coupled to a massless scalar field

TL;DR

This paper investigates the internal structure of rotating black holes with a massless scalar field, revealing that scalar radiation decay leads to null and spacelike singularities, with the scalar cloud causing unbounded curvature growth at the center.

Contribution

It introduces a late-time expansion method to analyze scalar field effects inside rotating black holes, showing the formation of singularities driven by scalar radiation.

Findings

Decaying scalar fluxes create a null singularity at the Cauchy horizon.

A central spacelike singularity forms at r=0 due to scalar cloud growth.

Curvature diverges exponentially with advanced time v near r=0.

Abstract

We employ a late-time expansion to study the interior of rotating black holes coupled to a massless scalar field in asymptotically flat spacetime. We find that decaying fluxes of scalar radiation into the black hole necessitate the existence of a null singularity at the Cauchy horizon and a central spacelike singularity at radius $r = 0$. In particular, the decaying influxes source a localized cloud of scalar radiation near $r=0$ whose amplitude grows unboundedly large as advanced time $v \to \infty$. The scalar cloud inevitably results in a central spacelike singularity at late times $v$, with the curvature near $r = 0$ diverging like $r^{-\alpha v}$, where $\alpha > 0$ is a constant.