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Abstract

Once detected, lensed gravitational waves will afford new means to probe the
matter distribution in the universe, complementary to electromagnetic signals.
Sources of continuous gravitational waves (CWs) are long-lived and stable,
making their lensing signatures synergic to short mergers of compact binaries.
CWs emitted by isolated neutron stars and lensed by Sgr A$^*$, the
super-massive black hole at the center of our galaxy, might be observable by
the next generation of gravitational wave detectors. However, it is unknown
under which circumstances these sources can be identified as lensed. Here we
show that future detectors can distinguish lensed CWs and measure all
parameters with precision $\sim 1-10\%$ for sources within $2-4$ Einstein radii
of Sgr A$^*$, depending on the source's distance. Such a detection, which
relies on the relative motion of the observer-lens-source system, can be
observed for transverse velocities above 3 km/s. Therefore, the chances of
observing strongly lensed neutron stars increase by one order of magnitude with
respect to previous estimates. Observing strongly lensed CWs will enable novel
probes of the galactic center and fundamental physics.