In this question I've mentioned an account of the recently reported 2nd observation of gravitational waves, LIGO and Virgo Collaborations, Phys. Rev. Lett. 116, 241103, 15 June 2016, where 1 of the 22 solar masses is said to have been converted into pure energy - gravitational waves.
My question here is in two parts:
- Is there any standard theoretical framework where this energy could - in any way - transfer back to more "familiar" forms of energy, where "familiar" means mechanical, electrical, thermal... things less exotic than the energy being stored in the vibration of space itself.
- Is there any discussion of one way this might actually come about. Sometimes a theory that says something is possible doesn't by itself make it very obvious how it would be possible.
I'm looking for something carefully worked out and published, and not interested in any discussion of practicality.
Answer
Feynman gave an argument of beads on a string or rod. The passage of a gravitational wave would cause the beads to move in a way similar to the arms of the LIGO interferometer. He argued that the motion might have friction on the string. We might think of this as magnets on a solonoid. If there are magnets at different places on the solonoid their motion would induce EMF by induction, and their motion would result in a net current and voltage across the solonoid.
Don't expect gravitational radiation to become any serious energy source. The coupling constant of gravitation is $8\pi G/c^4~=~4.12\times 10^{-45}N^{-1}$, which is very small. The Einstein field equation $G_{\mu\nu}~=$ $(8\pi G/c^4)T_{\mu\nu}$. For the right hand side the density of energy or momentum and the left curvature it is clear you need large curvatures to get large energy densities.
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