Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes

TL;DR

This paper proves the separability of massive vector fields in rotating black-hole spacetimes across dimensions, enabling detailed analysis of quasinormal modes and confirming previous numerical results.

Contribution

It establishes the separability of Proca equations in Kerr-NUT-(A)dS spacetimes, filling a key gap and enabling analytical study of vector perturbations.

Findings

Separability of Proca equations in higher-dimensional Kerr-NUT-(A)dS spacetimes.

Calculation of quasinormal modes for four-dimensional Kerr black holes.

Agreement with previous numerical studies on vector field perturbations.

Abstract

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in a perfect agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.