Long-Lived Quasinormal Modes and Quasi-Resonances around Non-Minimal Einstein-Yang-Mills Black Holes

TL;DR

This paper investigates the quasinormal modes of massive scalar fields around non-minimal Einstein-Yang-Mills black holes, revealing how field mass affects damping and stability, with new analytic formulas for large masses.

Contribution

It provides the first detailed computation of quasinormal frequencies in non-minimal Einstein-Yang-Mills black holes with a cosmological constant, including analytic formulas for large field masses.

Findings

Increasing scalar mass decreases damping rates.

Long-lived modes can exist in de Sitter black holes.

Scalar perturbations decay even with negative potential gaps.

Abstract

Using accurate computational methods, we compute the quasinormal frequencies of a massive scalar field propagating near a black hole in the framework of non-minimal Einstein-Yang-Mills theory with a non-zero cosmological constant. We show that increasing the mass of the scalar field significantly decreases the damping rate of the quasinormal modes for both asymptotically flat and de Sitter black holes. However, in the de Sitter case, arbitrarily long-lived modes can exist, whereas in the asymptotically flat case, the damping rate never vanishes completely. In the limit of quasi-resonances, we observe a kind of universal behavior where the frequencies do not depend on the coupling constant. Applying the time-domain integration of perturbation equations we show that even when the effective potential has a negative gap, the scalar field is stable and the perturbations decay in time. In the regime of large mass of the field we obtain the analytic formula for quasinormal modes.