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.

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

References in corpus (6)

• Asymptotic symmetries and subleading soft graviton theorem
• The gravitational-wave memory effect
• Asymptotic gravitational charges
• Hamiltonian derivation of dual gravitational charges
• A note on dual gravitational charges
• The First-Order Velocity Memory Effect from Compact Binary Coalescing Sources

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