Research Theme: Persistent GravitationalWave Observables
This post summarizes two papers about three new procedures by which one can measure generalized notions of gravitationalwave memory. The first paper was an Editors’ Suggestion in Phys. Rev. D, and it had a synopsis published about it in Physics.
Papers Highlighted

A. M. Grant and D. A. Nichols. “Persistent gravitationalwave observables: Curve deviation in asymptotically flat spacetimes.” Phys. Rev. D 105, 024056 (2022), arXiv:2109.03832.

E. E. Flanagan, A. M. Grant, A. I. Harte, and D. A. Nichols. “Persistent gravitationalwave observables: Nonlinear plane wave spacetimes.” Phys. Rev. D 101, 104033 (2020), arXiv:1912.13449.

E. E. Flanagan, A. M. Grant, A. I. Harte, and D. A. Nichols. “Persistent gravitationalwave observables: General framework.” Phys. Rev. D 99, 084004 (2019), arXiv:1901.00021.
Summary of the Papers
The gravitationalwave memory effect is often characterized by the lasting displacement it would cause between freely falling observers after a burst of gravitational waves pass by their locations. Subsequently, it was realized that there other types of memory effects that freely falling observers could measure, including lasting relative velocities, changes in proper time elapsed, and relative rotation of inertial gyroscopes. We were interested in determining procedures that observers could, in principle implement, by which observers could meaure all these memory effects (and potentially other new effects). We in fact found three such types of procedures, which encompass the known memory effects, and potentially other new ones. The first procedure involved measuring a type of deviation vector between two neary accelerating observers. The second involves transporting a certain kind of linear and angular momentum around a closed curve in spacetime. The third is based on measuring the location, linear momentum, and intrinsic angular momentum of a nearby spinning point particle. We called the outcome of these measurement procedures “persistent gravitationalwave observables,” and we are currently investigating their properties in specific gravitationalwave spacetimes.
The first class of spacetimes that we investigated were the socalled nonlinear planewave spacetimes. We found that several observables can be obtained from the values of tensors that solve the equation of geodesic deviation (specifically for observalbes that involved geodesic curves). Thus, these observables contain information that is equivalent to the displacement and subleading displacement (e.g., spin or center of mass) gravitationalwave memory effects. However, for observables involving worldlines with acceleration, the persistent observables were more nontrivial (and nonlocal) functions of the solutions to the equation of geodesic deviation and the acceleration of the curve. This implies that there are much wider range of possible persistent observables than the leading and subleading displacement memory effects (which will be investigated in greater detail in future work).
We then investigated the curvedeviation observable in asymptotically flat spacetimes. At leading order in distance from the source, we found that there is an infinite hierarchy of memory effects when the curvedeviation observable is measured by observers with a nontrival, timedependent acceleration. The entire collection of memory effects are sourced by “charge” and “flux” terms, where the flux part vanishes in the absence of gravitational waves. This chargeflux decomposition is well known for the displacement and subleading displacement (spin and center of mass) effects, but it was shown to hold for all of the accelerationdependent effects in this paper. For the effects that depend on higher derivatives of the initial acceleration, the charge and flux sources are more and more subleading parts of the expansion of the spacetime metric and curvature in a series in inverse distance. Thus, the curve deviation observable is capable of probing very highorder persistent changes in the spacetime through a measurement at large distances. This type of asymptotic reconstruction of the interior of a spacetime is reminiscent of the types of holography that appear in highenergy physics and string theory.