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In this paper, we examine the role played by topology, and some specificboundary conditions as well, on the physics of a higher-dimensional black hole.We analyze the line element of a five-dimensional non-extremalReissner-Nordstr\"{o}m black hole to obtain a new family of subspaces that aretypes of strong retractions and deformations, and then we extend these resultsto higher dimensions in order to deduce the relationship between various typesof transformations. We also study the scalar field perturbations in thebackground under consideration and obtain an analytical expression for thequasibound state frequencies by using the Vieira-Bezerra-Kokkotas approach,which uses the polynomial conditions of the general Heun functions, and then wediscuss the stability of the system and present the radial eigenfunctions. Ourmain goal is to discuss the physical meaning of these mathematical applicationsin such higher-dimensional effective metric.

On the five-dimensional non-extremal Reissner-Nordstr\"{o}m black hole: Retractions and scalar quasibound states