Maxwell perturbations in a cavity with Robin boundary conditions: two branches of modes with spectrum bifurcation on Schwarzschild black holes

TL;DR

This paper investigates Maxwell quasinormal modes in a cavity around Schwarzschild black holes, revealing two distinct mode sets and spectrum bifurcation effects similar to those in AdS black holes, through analytical and numerical methods.

Contribution

It introduces two boundary condition sets based on the vanishing energy flux principle and demonstrates spectrum bifurcation in Maxwell fields in a cavity, paralleling AdS black hole phenomena.

Findings

Two sets of Maxwell modes identified under different boundary conditions.

Analytical expressions for the imaginary parts of the modes derived.

Spectrum bifurcation occurs when the mirror is near the black hole horizon.

Abstract

We perform a systematic study of the Maxwell quasinormal spectrum in a mirror-like cavity following the generic Robin type vanishing energy flux principle, by starting with the Schwarzschild black holes in this paper. It is shown that, for black holes in a cavity, the vanishing energy flux principle leads to \textit{two} different sets of boundary conditions. By solving the Maxwell equations with these two boundary conditions both analytically and numerically, we observe \textit{two} distinct sets of modes. This indicates that the vanishing energy flux principle may be applied not only to asymptotically anti-de Sitter (AdS) black holes but also to black holes in a cavity. In the analytic calculations, the imaginary part of the Maxwell quasinormal modes are derived analytically for both boundary conditions, which match well with the numeric results. While in the numeric calculations, we complete a thorough study on the two sets of the Maxwell spectrum by varying the mirror radius $r_m$, the angular momentum quantum number $\ell$, and the overtone number $N$. In particular, we proclaim that the Maxwell spectrum may \textit{bifurcate} for both modes when the mirror is placed around the black hole event horizon, which is analogous to the spectrum bifurcation effects found for the Maxwell fields on asymptotically AdS black holes. This observation provides another example to exhibit the similarity between black holes in a cavity and the AdS black holes.