Mode-Coupling in Rotating Gravitational Collapse of a Scalar Field

TL;DR

This paper analytically investigates how rotation in Kerr black holes causes mode-coupling in scalar fields, leading to mixed modes and slower baldness compared to non-rotating black holes.

Contribution

It provides a detailed analytic analysis of mode-coupling effects caused by rotation in Kerr black holes, highlighting differences from Schwarzschild black holes.

Findings

Rotation induces mode mixing in scalar fields.

Late-time tails are dominated by different angular modes.

Rotating Kerr black holes become bald more slowly than Schwarzschild black holes.

Abstract

We present an analytic study of the mode-coupling phenomena for a scalar field propagating on a rotating Kerr background. Physically, this phenomena is caused by the dragging of reference frames, due to the black-hole (or star's) rotation. We find that different modes become mixed during the evolution and the asymptotic late-time tails are dominated by a mode which, in general, has an angular distribution different from the original one. We show that a rotating Kerr black hole becomes `bald' slower than a spherically-symmetric Schwarzschild black hole.