Late time tails in the Kerr spacetime

TL;DR

This paper investigates the late-time decay of perturbation fields in Kerr spacetime, confirming theoretical predictions through numerical analysis for small black hole spins.

Contribution

It provides a definitive numerical validation of theoretical predictions for late-time tails in Kerr spacetime with small spin parameter.

Findings

Decay rate matches theoretical predictions for small spin

Numerical results clarify controversy in previous studies

Supports the interpretation of multipole decay in Kerr spacetime

Abstract

Outside a black hole, perturbation fields die off in time as $1/t^n$. For spherical holes $n=2\ell+3$ where $\ell$ is the multipole index. In the nonspherical Kerr spacetime there is no coordinate-independent meaning of "multipole," and a common sense viewpoint is to set $\ell$ to the lowest radiatiable index, although theoretical studies have led to very different claims. Numerical results, to date, have been controversial. Here we show that expansion for small Kerr spin parameter $a$ leads to very definite numerical results confirming previous theoretical analyses.