Quasinormal resonances of a massive scalar field in a near-extremal Kerr black hole spacetime

TL;DR

This paper analytically derives the fundamental quasinormal resonances of massive scalar fields in near-extremal Kerr black holes, revealing how the resonance frequencies and damping rates depend on the scalar field mass.

Contribution

It provides the first analytical expressions for these resonances and identifies a critical mass parameter influencing the behavior of oscillation frequencies and damping rates.

Findings

Existence of a critical mass parameter $$ that affects resonance behavior.

Analytical formulas for resonance frequencies in near-extremal Kerr spacetime.

Numerical confirmation of the analytical results.

Abstract

The fundamental resonances of near-extremal Kerr black holes due to massive scalar perturbations are derived {\it analytically}. We show that there exists a critical mass parameter, $\mu_c$, below which increasing the mass $\mu$ of the field increases the oscillation frequency $\Re(\omega)$ of the resonance. On the other hand, above the critical field mass increasing the mass $\mu$ increases the damping rate $\Im(\omega)$ of the mode. We confirm our analytical results by numerical computations.