  Quasinormal modes are eigenmodes of dissipative systems. For instance, if a
spacetime with an event or cosmological horizon is perturbed from its
equilibrium state, quasinormal modes arise as damped oscillations with a
spectrum of complex frequencies, called quasinormal frequencies, that depends
just on the charges which define the geometry of the spacetime in which the
perturbation is propagating, such as the mass, electric charge, and angular
momentum. Mathematically, this discrete spectrum of quasinormal modes stems
from the fact that certain boundary conditions must be imposed to the physical
fields propagating in such a spacetime. In this thesis, we shall consider a
higher-dimensional generalization of the charged Nariai spacetime that is
comprised of the direct product of the two-dimensional de Sitter space, $dS_2$,
with an arbitrary number of two-spheres, $S^2$, and investigate the dynamics of
spin-$s$ field perturbations for $s = 0, 1/2, 1$ and $2$. The boundary
conditions leading to quasinormal modes are analyzed and the quasinormal
frequencies are analytically obtained.
