Charged particles in higher dimensional homogeneous gravitational field: Self-energy and self-force

TL;DR

This paper investigates the self-energy and self-force of charged particles in higher-dimensional homogeneous gravitational fields, deriving explicit formulas and analyzing divergences and regularizations up to eight dimensions.

Contribution

It provides new explicit expressions for self-energy and self-force in higher dimensions, including covariant regularization methods and analysis of logarithmic factors.

Findings

Self-energy divergence increases with dimensions.

Explicit self-force formulas up to eight dimensions.

Logarithmic factors ln(a) appear in odd dimensions.

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 usual electric charge and a case 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 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 a relation between the self-energy and self-force and obtain explicit expressions for the self-forces for the electric and scalar charge in the 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 both in the self-energy and 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.