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Poisson-Arago spot for gravitational waves

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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.

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Authors and Affiliations

  1. School of Physics and Technology, University of Jinan, Jinan, 250022, China

    HongSheng Zhang

  2. School of Physics and Technology, Wuhan University, Wuhan, 430072, China

    XiLong Fan

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  1. HongSheng Zhang
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  2. XiLong Fan
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Correspondence to XiLong Fan.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11922303, 11673008, 11075106, 11575083, and 11275128). XiLong Fan was also supported by the Hubei Province Natural Science Fund for the Distinguished Young Scholars (Grant No. 2019CFA052), and Newton International Fellowship Alumni Follow on Funding. HongSheng Zhang was also supported Shandong Province Natural Science Foundation (Grant No. ZR201709220395). The authors would like to thank the referees for their valuable comments which considerably improved the original text. The authors thank Yanbei Chen for valuable comments.

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Zhang, H., Fan, X. Poisson-Arago spot for gravitational waves. Sci. China Phys. Mech. Astron. 64, 120462 (2021). https://doi.org/10.1007/s11433-021-1764-y

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