Instability of the Proca field on Kerr spacetime

TL;DR

This paper investigates the instability of a massive vector boson (Proca) field around Kerr black holes, using advanced separation techniques to compute the bound state spectrum and analyze superradiant growth rates.

Contribution

It introduces a novel spectral method for solving the Proca field equations on Kerr spacetime and clarifies the relationship between different variable formalisms, advancing understanding of superradiant instabilities.

Findings

Calculated the bound state spectrum for the Proca field on Kerr spacetime.

Demonstrated that all three polarizations of the Proca field can be obtained from the FKKS ansatz.

Provided numerical estimates of the superradiant instability growth rates for various modes.

Abstract

A massive vector boson field in the vicinity of a rotating black hole is known to suffer an instability, due to the exponential amplification of (co-rotating, low-frequency) bound states by black hole superradiance. Here we calculate the bound state spectrum by exploiting the separation of variables recently achieved by Frolov, Krtous, Kubiznak and Santos (FKKS) for the Proca field on Kerr-(A)dS-NUT spacetimes of arbitrary dimension. Restricting to the 4D Kerr case, we first establish the relationship between the FKKS and Teukolsky variables in the massless case; obtain exact results for the angular eigenvalues in the marginally-bound case; and present a spectral method for solving the angular equation in the general case. We demonstrate that all three physical polarizations can be recovered from the FKKS ansatz, resolving an open question. We present numerical results for the instability growth rate for a selection of modes of all three polarizations, and discuss physical implications.