Late-time decay of scalar perturbations outside rotating black holes

TL;DR

This paper analytically derives the late-time decay rates of scalar fields around rotating Kerr black holes, revealing mode-dependent power-law tails and oscillations along the event horizon, differing from non-rotating cases.

Contribution

It introduces an analytic method to compute late-time decay tails of scalar perturbations in Kerr spacetime, highlighting differences from Schwarzschild black holes.

Findings

Power-law decay at all asymptotic regions

Decay indices differ from Schwarzschild values

Scalar field oscillates along the event horizon

Abstract

We present an analytic method for calculating the late-time tails of a linear scalar field outside a Kerr black hole. We give the asymptotic behavior at timelike infinity (for fixed $r$), at future null infinity, and along the event horizon (EH). In all three asymptotic regions we find a power-law decay. We show that the power indices describing the decay of the various modes at fixed $r$ differ from the corresponding Schwarzschild values. Also, the scalar field oscillates along the null generators of the EH (with advanced-time frequency proportional to the mode's magnetic number $m$).