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

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.

11 pages, 5 figures, published in EPJC

References in corpus (7)

• Quasi-Normal Modes and Gravitational Wave Astronomy
• Instability of Flat Space Enclosed in a Cavity
• Relating Black Hole Shadow to Quasinormal Modes for Rotating Black Holes
• Dirac perturbations on Schwarzschild-Anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes
• Maxwell quasinormal modes on a global monopole Schwarzschild-anti-de Sitter black hole with Robin boundary conditions
• Bifurcation of the Maxwell quasinormal spectrum on asymptotically anti-de Sitter black holes
• Charged Dirac perturbations on Reissner-Nordström-Anti-de Sitter spacetimes: quasinormal modes with Robin boundary conditions

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