Maxwell quasinormal modes on a global monopole Schwarzschild-anti-de Sitter black hole with Robin boundary conditions

TL;DR

This paper studies how a global monopole affects Maxwell quasinormal modes around Schwarzschild-anti-de Sitter black holes, deriving analytical and numerical results that reveal the monopole's influence on the spectrum and boundary conditions.

Contribution

It extends previous work by including a global monopole, deriving boundary conditions, and analyzing the monopole's effect on quasinormal modes both analytically and numerically.

Findings

Global monopole introduces two normal modes in pure AdS.

Monopole parameter causes a repulsive force affecting modes.

Quasinormal frequencies vary with angular momentum, overtone, and monopole strength.

Abstract

We generalize our previous studies on the Maxwell quasinormal modes around Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux boundary conditions, by adding a global monopole on the background. We first formulate the Maxwell equations both in the Regge-Wheeler-Zerilli and in the Teukolsky formalisms and derive, based on the vanishing energy flux principle, two boundary conditions in each formalism. The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole, and two different normal modes are obtained due to the existence of the monopole parameter. In the small black hole and low frequency approximations, the Maxwell quasinormal modes are solved perturbatively on top of normal modes by using an asymptotic matching method, while beyond the aforementioned approximation, the Maxwell quasinormal modes are obtained numerically. We analyze the Maxwell quasinormal spectrum by varying the angular momentum quantum number $\ell$, the overtone number $N$, and in particular, the monopole parameter $8\pi\eta^2$. We show explicitly, through calculating quasinormal frequencies with both boundary conditions, that the global monopole produces the repulsive force.