Low-frequency absorption cross section of the electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher dimensions

TL;DR

This paper calculates the low-frequency electromagnetic wave absorption cross section for extreme Reissner-Nordstrom black holes in higher dimensions, revealing mode dominance and upper bounds in certain dimensions.

Contribution

It provides exact solutions and transmission coefficients for electromagnetic waves in higher-dimensional black holes, highlighting mode mixing effects and establishing upper bounds.

Findings

Cross section dominated by l=2 modes rather than l=1

Exact solutions constructed for zero-frequency wave equations

Upper limit established for dimensions >6

Abstract

We investigate the low-frequency absorption cross section of the electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher dimensions. We first construct the exact solutions to the relevant wave equations in the zero-frequency limit. In most cases it is possible to use these solutions to find the transmission coefficients of partial waves in the low-frequency limit. We use these transmission coefficients to calculate the low-frequency absorption cross section in five and six spacetime dimensions. We find that this cross section is dominated by the modes with l=2 in the spherical-harmonic expansion rather than those with l=1, as might have been expected, because of the mixing between the electromagnetic and gravitational waves. We also find an upper limit for the low-frequency absorption cross section in dimensions higher than six.