High accuracy simulations of Kerr tails: coordinate dependence and higher multipoles

TL;DR

This paper uses high-precision numerical simulations to study how scalar fields decay over time around Kerr black holes, revealing that decay rates depend on coordinate choices and confirming theoretical predictions.

Contribution

It provides the first detailed numerical comparison of scalar field decay in Kerr spacetime across different coordinate systems, clarifying the influence of slicing on decay rates.

Findings

Decay rates depend on the coordinate slicing used.

Numerical results confirm theoretical predictions about decay behavior.

High-accuracy simulations distinguish between competing claims in the literature.

Abstract

We investigate the late time behavior of a scalar field on a fixed Kerr background using a 2+1 dimensional pseudospectral evolution code. We compare evolutions of pure axisymmetric multipoles in both Kerr-Schild and Boyer-Lindquist coordinates. We find that the late-time power-law decay rate depends upon the slicing of the background, confirming previous theoretical predictions for those decay rates. The accuracy of the numerical evolutions is sufficient to decide unambiguously between competing claims in the literature.