Wave Optics in Black Hole Spacetimes: Schwarzschild Case

TL;DR

This paper explores wave optics phenomena around Schwarzschild black holes, analyzing scattering, interference, and imaging effects using advanced mathematical techniques to understand wave behavior in curved spacetime.

Contribution

It introduces a detailed wave scattering analysis in Schwarzschild spacetime, incorporating Regge poles and the eikonal limit to improve understanding of wave effects near black holes.

Findings

Wave scattering characterized by Regge poles.

Interference effects between direct and winding rays.

Black hole imaging influenced by wave phenomena.

Abstract

We investigate the wave optics in the Schwarzschild spacetime. Applying the standard formalism of wave scattering problems, the Green function represented by the sum over the partial waves is evaluated using the Poisson sum formula. The effect of orbiting scattering due to the unstable circular orbit for null rays is taken into account as the contribution of the Regge poles of the scattering matrix and the asymptotic form of the scattering wave is obtained in the eikonal limit. Using this wave function, images of the black hole illuminated by a point source are reconstructed. We also discuss the wave effect in the frequency domain caused by the interference between the direct rays and the winding rays.