Poisson-Arago spot for gravitational waves

Abstract

For the observer at infinity, a Schwarzschild black hole serves as an attractive opaque disk with a radius of $$3\,\sqrt 3 M$$ that will produce the diffraction pattern of gravitational waves (GWs). In this study, we demonstrate that a bright spot, which is a diffraction effect analogous to the Poisson-Arago spot in optics, will appear when an ingoing (quasi-)plane GW is diffracted by a Schwarzschild black hole. Here, we propose the diffraction effect of the GWs described by the exact diffraction solution of the GWs using the Heun function. For the first time, the Fresnel half-wave zone method is proposed to calculate the angular part of the GW scattering stripes for the observer at infinity. The prospect of observing the diffraction bright spot is discussed with an eikonal approximation. For normal incidence (quasi)-plane waves with 100 Hz (0.1 Hz) frequency diffracted by the central black hole of the Milky Way, the time delay between the Earth bathed in a bright spot and the minimum of the first dark stripe is 3.86 (3860) d. We will witness the second bright fringe (40% amplitude of the central bright spot) after 6.2 (6200) d. This new diffraction pattern involving the early phase of inspirals and pulsars as continuous gravitational wave sources is a potential scientific target for future space-and ground-based gravitational wave detectors, respectively.