Smith–Will force in higher dimensions
We compute the self-energy of a static classical point-like charge (coupled with scalar or vector massless field), localized at the distance r ≫ rg outside the horizon of (n + 1)—dimensional Schwarzschild-Tangherlini black hole (n ≽ 3). We use the perturbation theory and obtain first orders for the static energy and corresponding self-force. Since the formal expression for self-energy diverges, for the computation we apply the dimensional-regularization technique, well-known in the quantum theory. In the lowest-dimensional cases the results are compared with those ones known in the literature. The difference between the odd and even dimensionalities is discussed as well.