Biconformal symmetry and static Maxwell fields near higher-dimensional black holes

TL;DR

This paper derives explicit static Maxwell Green functions near higher-dimensional Reissner-Nordstrom black holes using biconformal symmetry, providing new exact solutions and integral representations across various dimensions.

Contribution

It introduces a novel application of biconformal symmetry to obtain static Maxwell Green functions in higher-dimensional black hole spacetimes, including explicit solutions in five dimensions.

Findings

Derived relation between Green functions on Reissner-Nordstrom and Bertotti-Robinson backgrounds.

Obtained a simple integral representation for Green functions in arbitrary dimensions.

Provided exact static Green functions and vector potentials in five-dimensional spacetime.

Abstract

We study an electric field created by a static electric charge near the higher dimensional Reissner-Nordstrom black hole. The relation between the static Green functions on the D-dimensional Reissner-Nordstrom background and on the (D+2)-dimensional homogeneous Bertotti-Robinson spacetime is found. Using the biconformal symmetry we obtained a simple integral representation for the static Maxwell Green functions in arbitrary dimensions. We show that in a four-dimensional spacetime the static Green function obtained by the biconformal method correctly reproduces known results. We also found a closed form for the exact static Green functions and vector potentials in the five-dimensional Reissner-Nordstrom spacetime.