Persistent gravitational wave observables: General framework

Abstract

In the first paper in this series, we introduced "persistent gravitational wave observables" as a framework for generalizing the gravitational wave memory effect. These observables are nonlocal in time and nonzero in the presence of gravitational radiation. We defined three specific examples of persistent observables: a generalization of geodesic deviation that allowed for arbitrary acceleration, a holonomy observable involving a closed curve, and an observable that can be measured using a spinning test particle. For linearized plane waves, we showed that our observables could be determined just from one, two, and three time integrals of the Riemann tensor along a central worldline, when the observers follow geodesics. In this paper, we compute these three persistent observables in nonlinear plane wave spacetimes, and we find that the fully nonlinear observables contain effects that differ qualitatively from the effects present in the observables at linear order. Many parts of these observables can be determined from two functions, the transverse Jacobi propagators, and their derivatives (for geodesic observers). These functions, at linear order in the spacetime curvature, reduce to the one, two, and three time integrals of the Riemann tensor mentioned above. CONTENTS

The Poincaré and BMS flux-balance laws with application to binary systems

“…The supermomentum flux-balance law is associated with the displacement memory effect which is caused by a permanent displacement of C + between non-radiative regions due to null radiation reaching null infinity [24,38,45,46,48,49,78]. The super-angular momentum flux-balance law is associated with the super-angular momentum memory effect dubbed the "spin memory effect" [27,[58][59][60]. It is caused by an accumulation u 2 u 1 u∂ u C − between the initial and final retarded time of the operator u∂ u acting on the parity-odd radiative polarization mode.…”

“…The ten Poincaré flux-balance laws will be uniquely identified after providing the prescription for the angular momentum matching with [9,10,20,30,[33][34][35][36] and for the center-of-mass matching with [37]. The proper BMS flux-balance laws will be explicitly related to the three relevant memories defined from the Bondi shear, namely the displacement memory [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], the spin memory [27,[57][58][59][60] and the center-of-mass memory [28].…”

The Λ-BMS4 charge algebra

“…In asymptotically flat Einstein gravity, leading [1][2][3], subleading/overleading [4][5][6][7][8][9][10] or higher subleading/overleading [11,12] relationships have been found in the infrared sector, which relate symmetries [5,6,9,[13][14][15][16][17][18][19][20][21], memory effects [7,12,[22][23][24][25][26][27][28][29][30][31][32][33][34][35] and scattering identities involving soft modes [36,37]. Partial reviews include [38][39][40][41].…”

Infinite Towers of Supertranslation and Superrotation Memories

“…These considerations are preliminary and many gaps remain to be filled in. A connection with the results of [27][28][29] remains to be addressed. In addition, many extensions can be explored such as loop corrections, higher dimensional generalizations, coupling to matter and alternative gauge theories.…”