Massless field perturbations of the spinning C metric

TL;DR

This paper derives a master equation for spin $s\,\le2$ perturbations of the spinning C metric, analyzing horizon behavior, superradiance, and spin-acceleration coupling, extending Kerr spacetime results to accelerating rotating black holes.

Contribution

It introduces a unified master equation for gauge-invariant perturbations of the spinning C metric, including separation into radial and angular parts and analysis of superradiance effects.

Findings

Radial functions' behavior near horizons studied.

Modified spin-weighted spheroidal harmonics derived.

Coupling between spin and acceleration parameter discussed.

Abstract

A single master equation is given describing spin $s\le2$ test fields that are gauge- and tetrad-invariant perturbations of the {\it spinning C metric} spacetime representing a source with mass $M$, uniformly rotating with angular momentum per unit mass $a$ and uniformly accelerated with acceleration $A$. This equation can be separated into its radial and angular parts. The behavior of the radial functions near the horizons is studied and used to examine the influence of $A$ on the phenomenon of superradiance, while the angular equation leads to modified spin-weighted spheroidal harmonic solutions generalizing those of the Kerr spacetime. Finally the coupling between the spin of the perturbing field and the acceleration parameter $A$ is discussed.