Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena

TL;DR

This paper develops a Gupta-Bleuler quantization method for the electromagnetic field outside static black holes, and applies it to analyze low-energy phenomena such as charge response and wave absorption in various black hole spacetimes.

Contribution

It introduces a gauge-compatible quantization approach for electromagnetic fields around black holes and applies it to compute physical effects like absorption cross sections in higher dimensions.

Findings

Response rate of a static charge outside Schwarzschild black hole calculated.

Absorption cross sections for low-energy waves derived for higher-dimensional black holes.

Abstract

We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this field theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and extreme Reissner-Nordstr\"om black holes in arbitrary dimensions higher than three.