Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of self-dual black hole

J S Santos,M B Cruz,F A Brito

doi:10.1140/epjc/s10052-021-09884-1

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.

Highlights

General relativity (GR) [1] is accepted as the best description of gravitation physics
Considering gravitational perturbations the analyses have been made in [10,11], where the results showed for the first time in the context of black holes (BHs) in loop quantum gravity (LQG), a breaking of the isospectrality
The gravitational-wave observations have opened a new window to gravitational physics research

Summary

Introduction

General relativity (GR) [1] is accepted as the best description of gravitation physics. C (2021) 81:1082 the Immirzi parameter, a parameter measuring the quantum of the spacetime [8], a fundamental issue that remains open in this field In this context, the QNMs have been analyzed for the SDBH solution in [9], where the authors have considered the perturbations of the massless scalar field. To compute the QNMs we will use the WKB (Wentzel–Kramers–Brillouin) approach, which has been introduced by Schutz and Will [31], and after improved by Iyer and Will [32] and more recently by Konoplya [33,34], Matyjasek and Opala [35] and Hatsuda [36] In this context, we will study the influence of the parameters of LQG, the mass of the scalar field, and the nonminimal coupling with gravity in the QNMs, and in the stability of the SDBH solution.

Self-dual black hole

Scalar perturbations and effective potential

Quasinormal modes

Concluding remarks