Absorption cross sections of low energy photons for the Schwarzschild and extreme Reissner-Nordstrom black holes in arbitrary dimensions higher than three

Abstract

We examine the electromagnetic field quantization in static spherically symmetric spacetimes of arbitrary n dimensions in a modified Feynman gauge. This gauge is closely related to the A0 = 0 gauge and reduces to the Feynman gauge in Minkowski spacetime. The electromagnetic field equations in a black hole spacetime are not decoupled and are difficult to analyze in the Lorenz gauge. However, if we require the field to be divergence free on a (n – 2)-sphere (the spherical Coulomb gauge), the equations for the physical modes reduce to decoupled scalar field equations. Furthermore, solutions in terms of familiar special functions can be found in the low-energy regime. By using the electromagnetic field modes obtained in this modified Feynman gauge we calculate the low energy absorption cross sections of photons for the Schwarzschild and extreme Reissner-Nordstrom black holes in arbitrary dimensions higher than three.