Massive nonminimally coupled scalar field in Reissner-Nordstr\"om spacetime: Long-lived quasinormal modes and instability

TL;DR

This paper investigates the behavior of massive scalar fields with derivative coupling in Reissner-Nordström black hole spacetime, revealing long-lived quasinormal modes, stability conditions, and eikonal instability at high coupling.

Contribution

It demonstrates that long-lived quasinormal modes persist beyond test field approximation when derivative coupling is included, and identifies conditions for stability and instability.

Findings

Long-lived quasinormal modes exist with derivative coupling.

High coupling leads to eikonal instability.

Stable configurations show purely imaginary quasinormal modes.

Abstract

Here we show that the phenomenon of arbitrarily long-lived quasinormal modes (called quasiresonances) of a massive scalar field in the vicinity of a black hole is not an artifact of the test field approximation, but takes place also when the (derivative) coupling of a scalar field with the Einstein tensor is taken into consideration. We observe that at large coupling and high multipole numbers, the growing modes appear in the spectrum, which are responsible for the eikonal instability of the field. For small coupling, when the configuration is stable, there appear the purely imaginary quasinormal modes which are nonperturbative in the coupling constant. At the sufficiently small coupling the nonminimal scalar field is stable and the asymptotic late-time tails are not affected by the coupling term. The accurate calculations of quasinormal frequencies for a massive scalar field with the derivative coupling in the Reissner-Nordstr\"om black-hole background are performed with the help of Frobenius method, time-domain integration and WKB expansion.