Electrostatic self-force in the field of an ( n + 1)-dimensional black hole: Dimensional regularization
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, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Electrostatic Self-Force in the Field of an (n + 1)-Dimensional Black Hole: Dimensional Regularization Yu. V. Gratsa* and P. A. Spirina,b a Moscow
b
State University, Moscow, 119991 Russia Institute of Theoretical and Computational Physics, University of Crete, 71003 Heraklion, Greece *e-mail: [email protected] Received June 16, 2015
Abstract—The self-energy of a classical charged particle localized at a relatively large distance outside the event horizon of an (n + 1)-dimensional Schwarzschild–Tangherlini black hole for an arbitrary n ≥ 3 is calculated. An expression for the electrostatic Green function is derived in the first two orders of the perturbation theory. Dimensional regularization is proposed to be used to regularize the corresponding formally divergent expression for the self-energy. The derived expression for the renormalized self-energy is compared with the results of other authors. DOI: 10.1134/S1063776115120134
dimensions. It is believed that studying the exact solutions of the multidimensional generalizations of general relativity can shed light on some effects of the standard four-dimensional theory and will serve to better understand the latter. Such a study suggests an investigation of not only the geometrical peculiarities of the multidimensional generalizations of known solutions but also the dynamical features of classical and quantized matter on their background. Several examples of how differently the same effect can appear depending on the number (be it even or odd) of space dimensions are known already now. At the level of the self-force effect in the field of a black hole that we consider, some examples can be found in the literature cited below. The results of our study are yet another illustration of this fact. Another argument for the necessity of investigating multidimensional black holes provided in the literature is the AdS/CFT correspondence. It establishes a link between the properties of a multidimensional black hole and the quantum field theory in a space with dimensions less by one. A modern review of black hole physics can be found in the monograph [3]. A number of papers are devoted to a direct investigation of black holes and the necessity of their investigation in multidimensional general relativity (see, e.g., [4] and references therein). One of the problems of the classical field theory to which researchers have continually returned over more than one decade is the problem of the self-force of a classical charged particle in a curved spacetime. This problem is nontrivial even in the case of a charge at rest in an external static gravitational field [5]. The reason is that the effect is nonlocal. This manifests itself in the fact that the gravitational field distorts the
1. INTRODUCTION At present, black hole physics is a rapidly developing field of research. From the viewpoint of astrophysics, black holes are objects that may turn out to be responsible for many important processes in the Universe. For the theory of
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