Static Self-Forces in a Five-Dimensional Black Hole Spacetime

TL;DR

This paper derives explicit formulas for the electric and scalar fields of a static charge in a five-dimensional black hole spacetime and computes the resulting self-force, revealing it is independent of internal charge structure and arbitrary scales.

Contribution

It introduces an axiomatic regularization method that reduces the ambiguity in the self-force calculation in 5D black hole spacetimes, ensuring independence from arbitrary length scales.

Findings

Self-force is independent of internal charge structure.

Regularization reduces ambiguity in self-force calculations.

Explicit fields for static charges in 5D black hole spacetime derived.

Abstract

We obtain the electric field and scalar field for a static point charge in closed form in the 5D Schwarzschild-Tangherlini black hole spacetime. We then compute the static self-force in each of these cases by assuming that the appropriate singular field is a 4D Hadamard Green's function on the constant time Riemannian slice. It is well known that the Hadamard Green's function involves an arbitrary regular biscalar $W_{0}(x,x')$, whose coincidence limit $w(x)$ appears in the expression for the self-force. We develop an axiomatic approach to reduce this arbitrary function to a single arbitrary dimensionless coefficient. We show that in the context of this approach to regularization, the self-force does not depend on any undetermined length-scale and need not depend on the internal structure of the charge.