Abstract
A problem of self-energy and self-force for a charged point-like particle in a higher dimensional homogeneous gravitational field is considered. We study two cases, when a particle has the usual electric charge, and when it has a scalar charge, which is a source of a scalar massless minimally coupled field. We assume that a particle is at rest in the gravitational field, so that its motion is not geodesic, and it has an acceleration a directed away from the horizon. The self-energy of a point charge is divergent and the strength of the divergence grows with the number of dimensions. In order to obtain a finite contribution to the self-energy, we use a covariant regularization method which is a modification of the proper time cut-off and other covariant regularizations. We analyze the relation between the self-energy and the self-force and obtain explicit expressions for the self-forces for the electric and the scalar charge in spacetimes with the number of dimensions up to eight. General expressions for the case of higher dimensions are also obtained. We discuss special logarithmic factors ln a, which are present in both the self-energy and the self-force in odd dimensions. Finally, we compare the obtained results with the earlier known results both for the homogeneous gravitational field and for particles near black holes.
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Frolov, V.P., Zelnikov, A. Charged particles in higher dimensional homogeneous gravitational field: self-energy and self-force. J. High Energ. Phys. 2014, 68 (2014). https://doi.org/10.1007/JHEP10(2014)068
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DOI: https://doi.org/10.1007/JHEP10(2014)068