Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes

Abstract

The usual gravitational wave memory effect can be understood as a change in the separation of two initially comoving observers due to a burst of gravitational waves. Over the past few decades, a wide variety of other, "persistent" observables which measure permanent effects on idealized detectors have been introduced, each probing distinct physical effects. These observables can be defined in (regions of) any spacetime where there exists a notion of radiation, such as perturbation theory off of a fixed background, nonlinear plane wave spacetimes, or asymptotically flat spacetimes. Many of the persistent observables defined in the literature have been considered only in asymptotically flat spacetimes, and the perturbative nature of such calculations has occasionally obscured deeper relationships between these observables that hold more generally. The goal of this paper is to show how these more general results arise, and to do so we focus on two observables related to the separation between two, potentially accelerated observers. The first is the curve deviation, which is a natural generalization of the displacement memory, and also contains what this paper proposes to call drift memory (previously called "subleading displacement memory") and ballistic memory. The second is a relative proper time shift that arises between the two observers, either at second order in their initial separation and relative velocity, or in the presence of relative acceleration. The results of this paper are, where appropriate, entirely non-perturbative in the curvature of spacetime, and so could be used beyond leading order in asymptotically flat spacetimes.

The Precession Caused by Gravitational Waves

“…The full metric (1) contains numerous subleading corrections in 1/r, all of which we omit since they will play no role below. Crucially, all subleading terms are determined by leading metric data up to time-independent 'integration functions' on celestial spheres [19,37]. This is similar to mass and angular momentum, whose time evolution ( 2) is entirely fixed by news so that only the initial conditions m(u 0 , θ) and L a (u 0 , θ) are arbitrary.…”

The partial Bondi gauge: Further enlarging the asymptotic structure of gravity

“…It was shown in this context that the scattering amplitudes satisfy an infinite tower of soft theorems, which are in turn controlled by a higher spin symmetry [49][50][51][52][53][54]. Extending the known relationship between the spin-0 (mass) and spin-1 (angular momentum) charges, the leading and subleading soft theorems respectively, and the supertranslations and superrotations respectively, it was recently shown in [55] that there is indeed a spin-2 charge [56], related to a new type of asymptotic symmetries, whose asymptotic evolution equation is equivalent to the sub-subleading soft graviton theorem [57][58][59][60][61][62]. This hierarchy presumably extends to an infinite tower, and the properties of the charges and associated asymptotic symmetries are under active investigation.…”

“…They are responsible in the flat case for the leading, subleading, and sub-subleading soft graviton theorems respectively [55]. Interestingly, the spin-2 is also involved in a subleading symmetry and a class of memory observables which are non-local in time [56,170,171].…”

Gravitational memory effects and higher derivative actions

“…The confluence of a new era of gravitational wave astronomy [1] and a new understanding of the relationship [2][3][4][5][6][7][8][9] between generalized asymptotic BMS charges [10][11][12][13][14][15][16][17][18], and gravitational memory effects [19][20][21][22][23] has led to the tantalising possibility of using observations to constrain semi-classical effects in gravity [8,[24][25][26][27][28]. An important aspect of this new understanding is the expectation that any gravitational memory effect corresponds to an asymptotic charge generated by a particular asymptotic symmetry.…”