Maxwell perturbations on asymptotically anti-de Sitter spacetimes: Generic boundary conditions and a new branch of quasinormal modes

TL;DR

This paper investigates Maxwell perturbations on asymptotically AdS spacetimes, proposing vanishing energy flux boundary conditions that reveal a new branch of quasinormal modes, extending understanding of black hole stability and perturbation spectra.

Contribution

It introduces a physically motivated boundary condition based on energy flux, leading to the discovery of a new quasinormal mode branch in Maxwell perturbations on Kerr-AdS black holes.

Findings

Identified two Robin boundary conditions for Maxwell fields in AdS.

One boundary condition reproduces known quasinormal spectra.

The other reveals a new quasinormal mode branch.

Abstract

Perturbations of asymptotically Anti-de-Sitter (AdS) spacetimes are often considered by imposing field vanishing boundary conditions (BCs) at the AdS boundary. Such BCs, of Dirichlet-type, imply a vanishing energy flux at the boundary, but the converse is, generically, not true. Regarding AdS as a gravitational box, we consider vanishing energy flux (VEF) BCs as a more fundamental physical requirement and we show that these BCs can lead to a new branch of modes. As a concrete example, we consider Maxwell perturbations on Kerr-AdS black holes in the Teukolsky formalism, but our formulation applies also for other spin fields. Imposing VEF BCs, we find a set of two Robin BCs, even for Schwarzschild-AdS black holes. The Robin BCs on the Teukolsky variables can be used to study quasinormal modes, superradiant instabilities and vector clouds. As a first application, we consider here the quasinormal modes of Schwarzschild-AdS black holes. We find that one of the Robin BCs yields the quasinormal spectrum reported in the literature, while the other one unveils a new branch for the quasinormal spectrum.