Perturbations around the AdS Born-Infeld black holes

Abstract

We investigate the quasinormal mode of the perturbation of the scalar field interacting with the electromagnetic field in the backgrounds of neutral AdS black hole, the Reissner-Nordstrom AdS black hole, and the Born-Infeld AdS black hole. We study the influence of the electric charge $Q$, the coupling $q$ between electromagnetic and scalar field, and the Born-Infeld parameter $b$ on the quasinormal frequencies of the scalar perturbations. We observe the possible growing mode when the perturbation of the scalar field strongly couples to the electromagnetic field. When the electromagnetic field becomes nonlinear described by the Born-Infeld electrodynamics, the nonlinearity described by the Born-Infeld parameter can hinder the instability to happen in the scalar perturbation. The quasinormal behavior of the scalar field perturbation can help us further understand the physics in the holographic superconductor.