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Is it theoretically possible to detect gravitational lensing of both light and gravitational waves, when both originate from the same source/event (merger of two stellar black holes or merger of two neutron stars or merger of stellar black hole with the neutron star) when such merger is happening in neighboring to Milky Way galaxies and when both types of lensing are caused by the gravitational effect of the massive black hole located either in the center of that galaxy or the black hole of our Milky Way galaxy?

PS Though directional information contained in the captured time separated series of gravitational waves (together representing gravitational lensing of gravitational wave) is not accurate enough to corroborate directional information provided in observation of gravitational lensing of light in proving that both are generated by the same event, I am wondering whether calculation of the lens’ mass done separately for both observed spacial displacement (in case of gravitational lensing of light) and registered timing intervals (in case of gravitational lensing of gravitational wave), showing that the mass obtained in both types of calculation is about the same, - would provide more or less enough evidence to conclude with some level of confidence that both, gravitational lensing of light and gravitational lensing of gravitational wave are generated by the same event?

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Yes; typically, if the light is lensed, the gravitational waves are also lensed, and vice versa.

The main exception is if the lens is small. The current observatories, LIGO/Virgo/KAGRA, are sensitive to gravitational waves with wavelengths around 1000 km. That's a much longer wavelength than that of the light that we've detected from binary neutron star mergers. Waves diffract around objects that are much smaller than their wavelength, so the gravitational waves can diffract around small lenses that the light cannot.

For example, if the light and gravitational waves passed a stellar remnant black hole at a distance much closer than 1000 km, it could lens the light but not the gravitational waves. For those the interaction would be imperfectly but at least better characterized as scattering by a sub-wavelength particle due to diffraction.

However, that's not a concern for lensing by supermassive black holes. The event horizon of the black hole at the center of our galaxy is many millions of km in radius. It would lens the light and gravitational waves from a binary neutron star merger equally.

(Also, you mentioned merging of two black holes as an example of a source of light and gravitational waves. That would not work: merging of two black holes makes only gravitational waves and not light.)

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    $\begingroup$ Well, if the two black holes had accretion disks, then an optical burst could happen. $\endgroup$
    – eshaya
    Commented Jul 25, 2023 at 20:23
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    $\begingroup$ The question is, could you detect the lensing, in both cases? So, how does a gravity wave detector tell you that it was lensed? $\endgroup$
    – eshaya
    Commented Jul 25, 2023 at 20:25
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    $\begingroup$ @eshaya theory predictions for gravitational waveforms are really precise. So at least in the regime where wave optics are relevant (lens size comparable to wavelength), it should be pretty straightforward to tell if a signal was lensed (realistically you'd probably have to add lensed waveforms to your templates to avoid missing the events altogether). I'm not sure about the geometric optics limit -- you might not be able to infer from the gravitational waves alone that they are geometrically lensed (but maybe you could in combination with the light). $\endgroup$
    – Sten
    Commented Jul 25, 2023 at 20:48
  • $\begingroup$ @Sten "...add lensed waveforms to your templates to avoid missing the events altogether..." related: What does "GPU-accelerated butterfly matched filtering over dense bank of time-symmetric chirp-like templates" mean? (GW170817) $\endgroup$
    – uhoh
    Commented Jul 25, 2023 at 20:59
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    $\begingroup$ I guess there's also the question of whether we could even detect an electromagnetic counterpart through the noise of the galactic center. But the question does say "theoretically possible". $\endgroup$
    – Sten
    Commented Jul 25, 2023 at 21:06
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I also posted my question on https://www.quora.com/Is-it-possible-to-detect-gravitational-lensing-of-both-light-and-gravitational-waves-originating-from-the-same-event/ There I received an answer from AstroKevin92: "If two neutron stars merged, they would emit gravitational waves, a short gamma-ray burst, and optical afterglow from the ejected material. Exactly such a combined, multi-messenger detection was made in Aug 2017.

Now if this event just happened to have taken place and was visible to us via a gravitational lens we would still detect all 3 signals. But we would only see the lensing through the optical transmission because both gravitational wave detectors and gamma-ray detectors have poor directional resolution.

Put another way, the GW and gamma-ray images would be far too blurry to notice any lensing.

The Aug 2017 observations of gamma rays and gravitational waves happened within 2 seconds of each other, and an optical counterpart was found in the same part of the sky 11 hours later. It was clear enough that these were connected and part of the same event.

I would anticipate no fundamental difference if these events happened to have been lensed.

If there were multiple paths, then yes we would see the optical counterparts and the gravitational waves multiple times, which would strengthen the evidence that they are one and the same event."

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    $\begingroup$ Lensing has an effect on intensity not just on the spatial distribution of the radiation from a distant source. $\endgroup$
    – ProfRob
    Commented Aug 5, 2023 at 20:20

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