Nonlinear tails in the Kerr black hole ringdown

TL;DR

This paper analytically and numerically investigates nonlinear power law tails in Kerr black hole ringdowns, extending previous Schwarzschild results, and confirms the tail behavior through simulations.

Contribution

It extends the analytical understanding of nonlinear tails from Schwarzschild to Kerr black holes using the Teukolsky equation and confirms results with numerical simulations.

Findings

Nonlinear tails in Kerr black holes follow the same power laws as Schwarzschild.

Analytical derivation of tail power law $t^{- extstyle ext{ell} - eta - s}$.

Numerical simulations confirm the analytical tail behavior.

Abstract

Power law tails induced by nonlinearities of General Relativity (``sourced'' or ``nonlinear'' tails) were recently shown to dominate the late time waveform of Schwarzschild black hole ringdowns. We extend the analytical results regarding such nonlinear tails from Schwarzschild to Kerr black holes by studying the Teukolsky equation. Using a far field approximation to the radial Green's function, we analytically derived the tail power law to be $t^{-\ell-\beta-s}$ for spin-weight $s \neq 0$, harmonic mode $(\ell m)$ and source decay $r^{-\beta}$. We numerically confirmed these results for $\beta = 0, 1$. We also demonstrate the dynamical formation of such nonlinear tails for a massless scalar by numerically solving the Teukolsky equation. In all numerical results, Kerr black hole nonlinear tails have the same power laws as that for Schwarzschild black holes, as expected from the Minkowski nature of the spacetime in the far field region.