Source-Driven Tails in Kerr Spacetime: Nonlinear effects in Late-Time Behavior

TL;DR

This paper uses long-duration simulations to analyze nonlinear effects on late-time scalar-field tails in Kerr black hole spacetimes driven by outgoing sources, revealing a consistent increase in decay power-law indices compared to source-free cases.

Contribution

It extends previous Schwarzschild results to Kerr black holes, demonstrating that source-driven tails have decay indices larger by one unit, and provides detailed numerical analysis for various spins and multipolar sources.

Findings

Decay indices are larger by one compared to Price law.

Nonlinear source effects significantly alter late-time tail behavior.

Results are consistent with recent literature on gravitational wave tails.

Abstract

We present the long-duration time-domain simulations of scalar-field tails in Kerr spacetimes driven by \emph{outgoing} multipolar sources. Extending the recent work in the literature from Schwarzschild to rotating black holes, we evolve sources with $\ell'=\{0,1,2,3,4\}$ on backgrounds with dimensionless spin $a/M=\{0.0, 0.8, 1.0\}$ and extract the late-time decay rates of measured modes $\ell\le4$ for a nonlinearity-inspired outgoing source with a $1/r^2$ fall-off. In all cases we find the inverse power-law index $p_{\ell\ell'}$ to be larger than the source-free Price law values by one unit, i.e. $p^{\text{sourced}}_{\ell\ell'} = p^{\text{Price}}_{\ell\ell'} + 1$. We also include a power-law index value computation for a similar source-driven gravitational wave case $(\ell,m)=(4,4)$ and confirm closely related results in the recent literature.