Conversion of electromagnetic and gravitational waves by a charged black hole

TL;DR

This paper investigates how electromagnetic and gravitational waves convert into each other when interacting with charged black holes, providing detailed calculations of scattering and conversion cross sections across different wavelength regimes.

Contribution

It introduces a comprehensive analysis of wave conversion by charged black holes, combining numerical, Feynman-diagram, and geometric-optics methods to characterize the effect.

Findings

Conversion cross section matches Feynman calculations at long wavelengths

Converted flux can surpass scattered flux at large angles for highly-charged black holes

The scattering angle where fluxes are equal approaches 90 degrees in the extremal charge limit

Abstract

In a strong electromagnetic field, gravitational waves are converted into electromagnetic waves of the same frequency, and vice versa. Here we calculate the scattering and conversion cross sections for a planar wave impinging upon a Reissner-Nordstr\"om black hole in vacuum, using the partial-wave expansion and numerical methods. We show that, at long wavelengths, the conversion cross section matches that computed by Feynman-diagram techniques. At short wavelengths, the essential features are captured by a geometric-optics approximation. We demonstrate that the converted flux can exceed the scattered flux at large scattering angles, for highly-charged black holes. In the short-wavelength regime, the conversion effect may be understood in terms of a phase that accumulates along a ray. We compute the scattering angle for which the converted and scattered fluxes are equal, as a function of charge-to-mass ratio. We show that this scattering angle approaches $90$ degrees in the extremal limit.