---
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-Nordström black holes in arbitrary dimensions higher than three.'
address: |
    $^1$Instituto de Física Teórica, Universidade Estadual Paulista,\
    Rua Pamplona 145, 01405-900, São Paulo, São Paulo, Brazil\
    $^2$Departamento de Física, Universidade Federal do Pará,\
    Campus Universitário do Guamá, 66075-900, Belém, Pará, Brazil\
    $^3$Department of Mathematics, University of York,\
    Heslington, York YO10 5DD, United Kingdom
author:
- 'Luís C.B. Crispino$^{1,2}$, Atsushi Higuchi$^3$, and George E.A. Matsas$^1$'
title: ' Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena '
---

Introduction {#sec:Introduction}
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The prediction that black holes should thermally evaporate [@H] has sparked much interest in quantum field theory in 