Quasinormal modes of Reissner-Nordstr\"om-AdS black holes under physical field-vanishing boundary conditions

TL;DR

This paper introduces a physical boundary condition for RN-AdS black holes that requires both metric and electromagnetic perturbations to vanish at the boundary, leading to new spectral features in quasinormal modes.

Contribution

It proposes the physical field-vanishing boundary condition for RN-AdS black holes and derives its implications for quasinormal mode spectra.

Findings

Derived boundary conditions for master functions: Dirichlet for odd modes, Robin for even modes.

Computed quasinormal frequencies under the new boundary conditions.

Identified novel spectral features in the quasinormal mode spectrum.

Abstract

Boundary conditions play a key role in determining the perturbation behavior of a black hole. Motivated by two guiding principles for single-field perturbations -- the non-deformation of the boundary metric and the vanishing of electromagnetic energy flux at the AdS boundary -- we impose a boundary condition for Reissner-Nordstr\"om-AdS (RN-AdS) black holes requiring both the metric and electromagnetic field-strength perturbations to vanish at the AdS boundary, which we term the physical field-vanishing (PFV) condition. Using the formulas for perturbation reconstruction, we translate the PFV condition into boundary conditions on the master functions: Dirichlet-type for odd-parity modes and Robin-type for even-parity modes. With these boundary conditions, we compute the quasinormal frequencies of RN-AdS black holes and identify new spectral features. The PFV prescription introduced here could be applied to other multifield perturbation systems in asymptotically AdS spacetimes.