The Precession Caused by Gravitational Waves

Abstract

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.

arXiv comment6 pages, 3 figures. Short version of the long paper arXiv:2112.04535[hep-th]. v2: Minor typos fixed, published in PRL

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