universe Review Gravitational Lensing of Continuous Gravitational Waves Marek Biesiada 1,2, * and Sreekanth Harikumar 1   Citation: Biesiada, M.; Harikumar, S. Gravitational Lensing of Continuous Gravitational Waves. Universe 2021, 7, 502. https://doi.org/10.3390/ universe7120502 Academic Editors: Andrzej Królak and Paola Leaci Received: 5 November 2021 Accepted: 15 December 2021 Published: 17 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw, Poland; sreekanth.harikumar@ncbj.gov.pl 2 Department of Astronomy, Beijing Normal University, Beijing 100875, China * Correspondence: marek.biesiada@ncbj.gov.pl Abstract: Continuous gravitational waves are analogous to monochromatic light and could therefore be used to detect wave effects such as interference or diffraction. This would be possible with strongly lensed gravitational waves. This article reviews and summarises the theory of gravitational lensing in the context of gravitational waves in two different regimes: geometric optics and wave optics, for two widely used lens models such as the point mass lens and the Singular Isothermal Sphere (SIS). Observable effects due to the wave nature of gravitational waves are discussed. As a consequence of interference, GWs produce beat patterns which might be observable with next generation detectors such as the ground based Einstein Telescope and Cosmic Explorer, or the space-borne LISA and DECIGO. This will provide us with an opportunity to estimate the properties of the lensing system and other cosmological parameters with alternative techniques. Diffractive microlensing could become a valuable method of searching for intermediate mass black holes formed in the centres of globular clusters. We also point to an interesting idea of detecting the Poisson–Arago spot proposed in the literature. Keywords: gravitational waves; gravitational lensing; Poisson–Arago spot; interference; microlensing 1. Introduction With the first detection of gravitational waves (GWs) in 2015 from the coalescing compact binary system [1], we have entered the long-expected era of GW astronomy. A new window in the Universe has been opened. First, GW detections brought about the confirmation of the existence of binary black hole (BBH) systems in nature. A half of a century ago, the primary candidates for chirping signals were binary neutron stars (BNS) due to sober expectations based on Hulse–Taylor-like BNS systems discovered so far. Indeed, in 2017, the first of such coalescence was registered [2], and accompanying electromagnetic signals spanning from gamma rays through optical rays and radio waves were registered, allowing for the identification of the host galaxy and making a plethora of various other tests possible. Further observing runs of the LIGO–Virgo–KAGRA net- work considerably enriched the statistics of registered events. In the future, there will be a qualitative boost when the third generation of ground-based detectors such as the Einstein Telescope (ET) [3] or the Cosmic Explorer (CE) [4] as well as space-borne detectors (LISA, DECIGO, TianQin) [5–10] become operative. First, the sensitivity of ground-based detectors will be increased by an order of magnitude over the existing ones, allowing for the exploration of a larger volume of the universe by three orders of magnitude. Second, the satellite detectors will probe much lower frequencies of GWs (inaccessible from the ground due to seismic noise), enabling the observation of adiabatic inspiralling signals from binary systems much earlier than the coalescence phase probed by ground-based detectors. This means that besides the already registered chirp signals, we would gain access to almost monochromatic continuous GW signals. In this paper we discuss some new opportunities that will be available when continu- ous GW signals are registered. In the case of light, historically, there has been a dispute about its nature: corpuscular vs. wave. The wave nature of light has been established Universe 2021, 7, 502. https://doi.org/10.3390/universe7120502 https://www.mdpi.com/journal/universe