Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of Self-Dual Black Hole

TL;DR

This paper studies the quasinormal modes of a massive, nonminimally coupled scalar field in the spacetime of a Self-Dual Black Hole, revealing dependencies on field mass, coupling, and quantum gravity parameters, and indicating stability under small perturbations.

Contribution

It provides the first analysis of quasinormal modes for a nonminimally coupled scalar field in a loop quantum black hole spacetime using the 3rd order WKB method.

Findings

Self-Dual Black Hole is stable under scalar perturbations for small parameters.

Quasinormal modes vary with scalar field mass and coupling, indicating possible conformal symmetry breaking.

Results depend strongly on loop quantum gravity parameters.

Abstract

In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the Self-Dual Black Hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the Loop Quantum Gravity. From our results, we can check that the Self-Dual Black Hole is stable under the scalar perturbations when assuming small values for the parameters. Also, such results tell us that the quasinormal modes assume different values for the cases where the mass of field is null and the nonminimal coupling assumes $\xi=0$ and $\xi=1/6$, i.e., a possible breaking of the conformal invariance can be seen in the context of loop quantum black holes.