Brief note on high-multipole Kerr tails

TL;DR

This paper investigates the late-time decay rates of scalar fields in Kerr black hole backgrounds, extending numerical analysis to high multipoles and extremal cases, confirming recent theoretical predictions.

Contribution

The authors enhance a time-domain Teukolsky code to accurately compute decay rates for multipoles up to 16 in Kerr spacetime, including extremal cases, validating recent decay expressions.

Findings

Decay rates agree with recent theoretical predictions for  multipoles.

Horizon tails in extremal Kerr follow null infinity decay expressions.

Reliable numerical decay rates obtained for multipoles up to 16.

Abstract

In this note we reconsider the late-time, power-law decay rate of scalar fields in a Kerr space-time background. We implement a number of mathematical and computational enhancements to our time-domain, (2+1)D Teukolsky evolution code and are able to obtain reliable decay rates for multipoles as high as $\ell=16$. Our numerical results suggest full agreement with the proposed decay expressions in recent work for both the finite distance, and null infinity cases. We also study the same in the context of extremal Kerr space-time and find that the same results hold, except that the horizon tails follow the null infinity expressions instead.