Calculating Differential Precession of Gyroscopes Due to Gravitational Waves

[WannabeNewton]

To motivate the question, Andy Strominger recently put out a paper on calculating the Sagnac shift of counterrotating beams due to the angular momentum flux of a passing gravitational wave.

See here: http://arxiv.org/abs/1502.06120.

But consider now two nearby freely falling gyroscopes initially at rest in some background inertial frame and a weak gravitational wave passing by them. Is there a way to compute the differential precession of the gyroscopes due to the angular momentum of the gravitational wave, say by looking at the magnetic part of the Riemann tensor and/or the twist of a congruence of freely falling gyroscopes? Has such a calculation been done in the literature?

To clarify, I don't mean the precession of a single gyroscope relative to the axes of the TT-gauge coordinates.

Furthermore, would there also be a memory effect after the gravitational wave has gone to future null infinity, say in terms of a permanent relative shift of the gyroscopes' axes?

 

[Mentz114]

This topic is way beyond my technical ability but the paper you refer to has a section on the memory effect where two inertial objects can be permanently moved apart ( and together ) by a passing energy pulses. I may have misinterpreted that so please correct me if necessary.

I was struck by two possible effects

1. Galaxy formation via collapse of a gigantic hydrogen cloud is affected by sound waves with colossal wavelengths which cause compressed regions where star formation is accelerated. Could GWs do this ?

2. the matter distribution just before transparency could also be affected, imprinting on the CMB.