Self-force on a charge outside a five-dimensional black hole

Abstract

We compute the electromagnetic self-force acting on a charged particle held in place at a fixed position r outside a five-dimensional black hole described by the Schwarzschild-Tangherlini metric. Using a spherical-harmonic decomposition of the electrostatic potential and a regularization prescription based on the Hadamard Green's function, we express the self-force as a convergent mode sum. The self-force is first evaluated numerically, and next presented as an analytical expansion in powers of R/r, with R denoting the event-horizon radius. The power series is then summed to yield a closed-form expression. Unlike its four-dimensional version, the self-force features a dependence on a regularization parameter s that can be interpreted as the particle's radius. The self-force is repulsive at large distances, and its behavior is related to a model according to which the force results from a gravitational interaction between the black hole and the distribution of electrostatic field energy attached to the particle. The model, however, is shown to become inadequate as r becomes comparable to R, where the self-force changes sign and becomes attractive. We also calculate the self-force acting on a particle with a scalar charge, which we find to be everywhere attractive. This is to be contrasted with its four-dimensional counterpart, which vanishes at any r.

26 pages, 2 figures. Major changes from previous version: the regularization procedure is now fully justified, and the singular field is shown to make a contribution to the self-force

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• Self-force from conical singularity, without renormalization
• Static Self-Forces in a Five-Dimensional Black Hole Spacetime
• Aspects of electrostatics in BTZ geometries
• Self-force on a static particle near a black hole
• Self-force as a probe of global structure
• Self-action in Gravity
• The inverse spatial Laplacian of spherically symmetric spacetimes
• Scalar Wave Tails in Even Dimensional Weakly Curved Static Newtonian Spacetimes