Radiative falloff in the background of rotating black hole

TL;DR

This paper numerically investigates the late-time decay of linear fields with various spins in a rotating black hole background, revealing mode dominance patterns influenced by black hole spin and initial data symmetry.

Contribution

It introduces a numerical method using ingoing Kerr coordinates to analyze late-time tails of linear fields in rotating black holes, highlighting mode dominance based on initial conditions.

Findings

Late-time tails are dominated by the mode with the least multipole moment.

Mode dominance depends on the equatorial symmetry of initial data.

The analysis covers fields with any spin in Kerr black hole backgrounds.

Abstract

We study numerically the late-time tails of linearized fields with any spin $s$ in the background of a spinning black hole. Our code is based on the ingoing Kerr coordinates, which allow us to penetrate through the event horizon. The late time tails are dominated by the mode with the least multipole moment $\ell$ which is consistent with the equatorial symmetry of the initial data and is equal to or greater than the least radiative mode with $s$ and the azimuthal number $m$.