Re: detect gravitational waves
Check out the LIGO web site, and the FAQs at https://www.ligo.caltech.edu/page/faq?highlight=How%20does%20LIGO%20work?
"If a gravitational wave stretches the distance between the LIGO mirrors, doesn't it also stretch the wavelength of the laser light?
While it's true that a gravitational wave does stretch and compress the wavelength of the light in the arms ever so slightly, it does NOT affect the fact that the beams will travel different distances as the wave changes each arm's length. And the only thing that matters to LIGO is how far the beams travel in each arm before being merged once again.
LIGO is designed so that as long as the distance the laser beams travel is exactly the same in both arms, they will make their trips in exactly the same time. When recombined, the beams totally destructively interfere with each other. In other words, they cancel each other out and no light emerges from the instrument. When this is occurring, we know the interferometer and its components are stable and the Universe is quiet.
Suddenly, a gravitational wave passes! What happens?
A gravitational wave causes each of LIGO's arms to change length in an opposite fashion, i.e., when one arm gets longer, the other gets shorter. Then they switch--the longer arm becomes the shorter arm and the shorter arm becomes the longer arm. This opposite oscillation in length occurs for as long as the waves pass, one getting longer while the other shorter, then vice versa, and so on, until the waves dissipate.
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LISA is basically 'LIGO in Spaaaace'.
Incidentally, if you have any questions about LIGO or black holes, there is an Ask LIGO page where a LIGO boffin will explain things (as far as possible) in lay terms. Very useful for anyone without a Nobel prize in cosmology.