Diffusion of the electromagnetic energy due to the backscattering off Schwarzschild geometry

TL;DR

This paper analyzes how electromagnetic waves scatter off Schwarzschild spacetime curvature, quantifying the backscattered energy depending on initial conditions and wave frequency, with implications for scalar fields and gravitational waves.

Contribution

It provides a compact formula estimating backscattered electromagnetic energy in Schwarzschild spacetime, highlighting dependence on wave frequency and initial parameters.

Findings

Backscattered energy is significant in long wave regimes.

Short wave limit renders backscattering negligible.

Results extend to scalar fields and potentially gravitational waves.

Abstract

Electromagnetic waves propagate in the Schwarzschild spacetime like in a nonuniform medium with a varying refraction index. A fraction of the radiation scatters off the curvature of the geometry. The energy of the backscattered part of an initially outgoing pulse of electromagnetic radiation can be estimated, in the case of dipole radiation, by a compact formula depending on the initial energy, the Schwarzschild radius and the pulse location. The magnitude of the backscattered energy depends on the frequency spectrum of the initial configuration. This effect becomes negligible in the short wave limit, but it can be significant in the long wave regime. Similar results hold for the massless scalar fields and are expected to hold also for weak gravitational waves.