Self-energy of a scalar charge near higher-dimensional black holes

TL;DR

This paper investigates the self-energy of scalar charges near higher-dimensional black holes, revealing that corrections depend on the spacetime dimension and are related to conformal anomalies.

Contribution

It provides an exact calculation of the self-energy correction for scalar charges in higher-dimensional black hole spacetimes, highlighting the dimensional dependence of these corrections.

Findings

Self-energy correction is zero in even dimensions.

Non-zero correction appears in odd dimensions.

The correction is linked to conformal anomalies.

Abstract

We study the problem of self-energy of charges in higher dimensional static spacetimes. Application of regularization methods of quantum field theory to calculation of the classical self-energy of charges leads to model-independent results. The correction to the self-energy of a scalar charge due to the gravitational field of black holes of the higher dimensional Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in even dimensions, but it acquires non-zero value in odd dimensional spacetimes. The origin of the self-energy correction in odd dimensions is similar to the origin the conformal anomalies in quantum field theory in even dimensional spacetimes.