Gyroscopic Gravitational Memory

Abstract

We study the motion of a gyroscope located far away from an isolated gravitational source in an asymptotically flat space-time. 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. The effect is related to asymptotic symmetries: at leading order in the inverse distance to the source, the precession rate coincides with the (covariant) dual mass aspect, providing a celestially local measurement protocol for dual supertranslation charges. Furthermore, the net gyroscopic memory is derived from flux-balance equations for superrotations and contains an extra flux generating electric-magnetic duality. The spin memory effect is reproduced as a special case.

Gravitational memory effects and higher derivative actions

“…Another type of observable that an observer can measure is the orientation of a freely falling gyroscope in her lab and how it is affected by GWs. This was considered in [64,65]. Consider a small freely falling gyroscope with proper velocity V µ , given by equation ( 15), and spin S µ .…”

“…The physical observable that is of particular interest here is the precession of a freelyfalling gyroscope in the asymptotic region of spacetime caused by gravitational waves [64,65], and a net rotation after the passage of gravitational wave dubbed the 'gyroscopic memory effect'. As noted in Refs.…”

“…As noted in Refs. [64,65], the expression for the gyroscopic memory effect is clearly related to dual quantities. However, it is not equal to any of the dual charges previously derived.…”

“…In this subsection we introduce the radial kick memory and review briefly the gyroscopic memory effect of Ref. [64,65]. In section 3, we review the higher derivative charges derived in Ref.…”

Higher derivative asymptotic charges and internal Lorentz symmetries

“…[2,12], charges that appear at subleading orders may be important and ought not be dismissed. The plethora of potentially observable gravitational memory effects [13][14][15][16][17] and their relation to asymptotic symmetries and charges [18] makes it all the more important to investigate all the possible asymptotic charges.…”