Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes

Gravitational-wave (GW) memory effects are constant changes in the GW strain and its time integrals, which are closely connected to changes in the charges that characterize asymptotically flat spacetimes. The first GW memory effect discovered was a lasting change in the GW strain. It can occur when GWs or massless fields carry away 4-momentum from an isolated source. Subsequently, it was shown that fluxes of intrinsic angular momentum can generate a new type of memory effect called the spin memory, which is an enduring change in a portion of the time integral of the GW strain. In this paper, we note that there is another new type of memory effect. We call it the “center-of-mass (CM) memory effect,” because it is related to changes in the CM part of the angular momentum of a spacetime. We first examine a few properties of the CM angular momentum. Specifically, we describe how it transforms under the supertranslation symmetry transformations of the Bondi-Metzner-Sachs group, and we compute a new expression for the flux of CM angular momentum carried by GWs in terms of a set of radiative multipole moments of the GW strain. We then turn to the CM memory effect. The CM memory effect appears in a quantity which has the units of the time integral of the GW strain. We define the effect in asymptotically flat spacetimes that start in a stationary state, radiate, and settle to a different stationary state. We show that it is invariant under infinitesimal supertranslation symmetries in this context. To determine the magnitude of the flux of CM angular momentum and the CM memory effect, we compute these quantities for nonspinning, quasicircular compact binaries in the post-Newtonian approximation. The CM memory effect arises from terms in the gravitational waveform for such binaries beginning at third and fourth post-Newtonian order for unequal- and equal-mass binaries, respectively. Finally, we estimate the amplitude of the CM memory effect for these binaries. We anticipate that it will be unlikely for current or upcoming GW detectors to measure the effect.