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Smith–Will force in higher dimensions

    https://doi.org/10.1142/9789813226609_0325Cited by:0 (Source: Crossref)
    Abstract:

    We compute the self-energy of a static classical point-like charge (coupled with scalar or vector massless field), localized at the distance rrg 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.