High-order tail in Kerr spacetime

TL;DR

This paper develops an analytical method to compute the late-time decay tail of linear field perturbations in Kerr spacetime, revealing detailed power-law and logarithmic corrections for scalar fields.

Contribution

It introduces a formalism for calculating high-order late-time tails for arbitrary integer spin fields in Kerr spacetime, extending previous results.

Findings

Leading order tail: $t^{-2 ext{l}-3}$ decay

Third order correction: $t^{-2 ext{l}-5} ext{ln} t$ tail

Applicable to general integer spin fields

Abstract

We investigate the late-time tail of the retarded Green function for the dynamics of a linear field perturbation of Kerr spacetime. We develop an analytical formalism for obtaining the late-time tail up to arbitrary order for general integer spin of the field. We then apply this formalism to obtain the details of the first five orders in the late-time tail of the Green function for the case of a scalar field: to leading order we recover the known power law tail $t^{-2\ell-3}$, and at third order we obtain a logarithmic correction, $t^{-2\ell-5}\ln t$, where $\ell$ is the field multipole.