  The electromagnetic and gravitational quasinormal spectra of
$(3+1)$-dimensional plane-symmetric anti-de Sitter black holes are analyzed in
the context of the AdS/CFT correspondence. According to such a correspondence,
the electromagnetic and gravitational quasinormal frequencies of these black
holes are associated respectively to the poles of retarded correlation
functions of $R$-symmetry currents and stress-energy tensor in the
holographically dual conformal field theory: the $(2+1)$-dimensional
$\mathcal{N}=8$ super-Yang-Mills theory. The connection between AdS black holes
and the corresponding field theory is used to unambiguously fix the boundary
conditions that enter the proper definition of quasinormal modes. Such a
procedure also helps one to decide, among the various different possibilities,
what are the appropriate gauge-invariant quantities one should use in order to
correctly describe the electromagnetic and gravitational blackhole
perturbations. These choices imply in different dispersion relations for the
quasinormal modes when compared to some of the results in the literature. In
particular, the long-distance, low-frequency limit of dispersion relations
presents the characteristic hydrodynamic behavior of a conformal field theory
with the presence of diffusion, shear, and sound wave modes. There is also a
family of purely damped electromagnetic modes which tend to the bosonic
Matsubara frequencies in the long-wavelength regime.
