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The Precession Caused by Gravitational Waves

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arxiv 2203.16216 v2 pith:3SM2S4IM submitted 2022-03-30 gr-qc hep-th

The Precession Caused by Gravitational Waves

classification gr-qc hep-th
keywords effectgravitationalanglememoryprecessionratewavesarcseconds
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We show that gravitational waves cause freely falling gyroscopes to precess relative to fixed distant stars, extending the stationary Lense-Thirring effect. The precession rate decays as the square of the inverse distance to the source, and is proportional to a suitable Noether current for dual asymptotic symmetries at null infinity. Integrating the rate over time yields a net rotation -- a `gyroscopic memory' -- whose angle reproduces the known spin memory effect but also contains an extra contribution due to the generator of gravitational electric-magnetic duality. The angle's order of magnitude for the first LIGO signal is estimated to be $\Phi\sim 10^{-35}$ arcseconds near Earth, but the effect may be substantially larger for supermassive black hole mergers.

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