The perturbations of fields with spin 0, 1/2, and 1 propagating in a higher-dimensional generalization of the charged Nariai spacetime are investigated. The boundary conditions leading to quasinormal modes are analyzed and the quasinormal frequencies are analytically obtained.

The field equation for a spin 1/2 massive charged particle propagating in spacetimes that are the direct product of 2-dimensional spaces is separated. Moreover, we use this result to attain the separability of the Dirac equation in some specific static black hole solutions whose horizons have topology R × S 2 × · · · × S 2 .

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In this work we analytically obtain the quasinormal spectrum for the gravitational perturbation on a higher-dimensional generalization of the Nariai spacetime that is comprised of the direct product of the two-dimensional de Sitter space with several two-spheres. A key step in order to attain this result is to use a suitable basis for the angular functions depending on the rank of the tensorial degree of freedom that one needs to describe. Here we define such a basis, which is a generalization of the tensor spherical harmonics that is suited for spaces that are the product of several spaces of constant curvature.

The exact electrically charged solutions to the Dirac equation in higherdimensional generalized Nariai spacetimes are obtained. Using these solutions, the boundary conditions leading to quasinormal modes of the Dirac field are analyzed, and their correspondent quasinormal frequencies are analytically calculated.