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We perform a systematic study of the Maxwell quasinormal spectrum in amirror-like cavity following the generic Robin type vanishing energy fluxprinciple, by starting with the Schwarzschild black holes in this paper. It isshown that, for black holes in a cavity, the vanishing energy flux principleleads to \textit{two} different sets of boundary conditions. By solving theMaxwell equations with these two boundary conditions both analytically andnumerically, we observe \textit{two} distinct sets of modes. This indicatesthat the vanishing energy flux principle may be applied not only toasymptotically anti-de Sitter (AdS) black holes but also to black holes in acavity. In the analytic calculations, the imaginary part of the Maxwellquasinormal modes are derived analytically for both boundary conditions, whichmatch well with the numeric results. While in the numeric calculations, wecomplete a thorough study on the two sets of the Maxwell spectrum by varyingthe mirror radius $r_m$, the angular momentum quantum number $\ell$, and theovertone number $N$. In particular, we proclaim that the Maxwell spectrum may\textit{bifurcate} for both modes when the mirror is placed around the blackhole event horizon, which is analogous to the spectrum bifurcation effectsfound for the Maxwell fields on asymptotically AdS black holes. Thisobservation provides another example to exhibit the similarity between blackholes in a cavity and the AdS black holes.

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