Modos quase normais de um campo escalar massivo acoplado não-minimamente à gravidade no espaço-tempo do buraco negro auto-dual.

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 WKB approach, where we can verify a strong dependence on the mass of scalar field, the parameter of nonminimal coupling with gravity, and the 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 ξ = 0 and ξ = 1/6, i.e., a possible breaking of the conformal invariance can be seen in the context of Self-Dual Black Hole.