  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory