Gyroscopic gravitational memory

Abstract

We study the motion of a gyroscope located far away from an isolated gravitational source in an asymptotically flat spacetime. As seen from a local frame tied to distant stars, the gyroscope precesses when gravitational waves cross its path, resulting in a net ‘orientation memory’ that carries information on the wave profile. At leading order in the inverse distance to the source, the memory consists of two terms: the first is linear in the metric perturbation and coincides with the spin memory effect, while the second is quadratic and measures the net helicity of the wave burst. Both are closely related to symmetries of the gravitational radiative phase space at null infinity: spin memory probes superrotation charges, while helicity is the canonical generator of local electric-magnetic duality on the celestial sphere.

Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes

“…Finally, this series of papers has had as its primary focus the three observables defined in Paper I: the curve deviation, the angular momentum holonomy, and finally an observable defined in terms of spinning test particles. However, there are a plethora of other observables which have been considered in the literature, such as the Sagnac-interferometer observable which served as the original definition of the spin memory [16], or the orientation of a gyroscope relative to a fixed, fiducial orientation [33,34]. Much like the analysis in this paper of the proper time observable of [14], it would be valuable to perform nonlinear analyses of these observables as well.…”

“…Since Paper I, several new persistent observables have been defined [30][31][32][33][34][35]. Of interest to this paper is that many of these effects have been considered only in asymptotically flat spacetimes.…”

On the gravitational precession memory effect for an ensemble of gyroscopes

“…The first term of ∆Φ is similar to what appears in the spin memory effect, given by the difference ∆T in travel time T of the two beams, and is the effect of gravitational waves on a Sagnac interferometer [12]. The second nonlinear term is related to the charge of gravitational electric-magnetic duality, as shown in [16,17]. Any index with a hat represent the index in the local frame.…”

“…the celestial sphere), source oriented local frame is defined as the one with its time-like vector along the retarded time u. Through a spatial rotation, this local frame can be tied to the distant stars [16,17]. Using these considerations it is shown [16,17,20] that as an effect of the gravitational wave passage, a gyroscope initially oriented in an arbitrary direction, S î(u 0 ), would experience (up to O(r −2 )) a net precession…”

“…The displacement memory effect [7,8], the most known one, emerges as a net displacement between freely falling test particles in the wave zone. There are other effects such as kick memory [9,10], spin memory [11][12][13], center-of-mass memory [14], and gyroscopic memory [15][16][17] appearing in different contexts.…”