3D simulations of linearized scalar fields in Kerr spacetime

TL;DR

This paper studies the late-time decay of scalar fields in Kerr spacetime using 3D spectral simulations, comparing different initial data setups and analyzing their influence on decay behavior.

Contribution

It presents a detailed numerical analysis of scalar field decay in Kerr spacetime, highlighting differences in intermediate evolution based on initial data coordinate choices.

Findings

Late-time decay rates are consistent across different initial data.

Intermediate evolution can vary significantly depending on initial data coordinates.

Spectral methods effectively model scalar field dynamics in Kerr spacetime.

Abstract

We investigate the behavior of a dynamical scalar field on a fixed Kerr background in Kerr-Schild coordinates using a 3+1 dimensional spectral evolution code, and we measure the power-law tail decay that occurs at late times. We compare evolutions of initial data proportional to f(r) Y_lm(theta,phi) where Y_lm is a spherical harmonic and (r,theta,phi) are Kerr-Schild coordinates, to that of initial data proportional to f(r_BL) Y_lm(theta_BL,phi), where (r_BL,theta_BL) are Boyer-Lindquist coordinates. We find that although these two cases are initially almost identical, the evolution can be quite different at intermediate times; however, at late times the power-law decay rates are equal.