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

Abstract

Asymptotically flat spacetimes admit both supertranslations and Lorentz transformations as asymptotic symmetries. Furthermore, they admit super-Lorentz transformations, namely superrotations and superboosts, as outer symmetries associated with super-angular momentum and super-center-of-mass charges. In this paper, we present comprehensively the flux-balance laws for all such BMS charges. We distinguish the Poincaré flux-balance laws from the proper BMS flux-balance laws associated with the three relevant memory effects defined from the shear, namely, the displacement, spin and center-of-mass memory effects. We scrutinize the prescriptions used to define the angular momentum and center-of-mass. In addition, we provide the exact form of all Poincaré and proper BMS flux-balance laws in terms of radiative symmetric tracefree multipoles. Fluxes of energy, angular momentum and octupole super-angular momentum arise at 2.5PN, fluxes of quadrupole supermomentum arise at 3PN and fluxes of momentum, center-of-mass and octupole super-center-of-mass arise at 3.5PN. We also show that the BMS flux-balance laws lead to integro-differential consistency constraints on the radiation-reaction forces acting on the sources. Finally, we derive the exact form of all BMS charges for both an initial Kerr binary and a final Kerr black hole in an arbitrary Lorentz and supertranslation frame, which allows to derive exact constraints on gravitational waveforms produced by binary black hole mergers from each BMS flux-balance law.

Multipole expansion of gravitational waves: from harmonic to Bondi coordinates

“…Recent interest in Bondi gauge arose from the fact that it is preserved under an infinite set of residual symmetries, dubbed the generalized BMS group, that is generated by supertranslations and arbitrary diffeomorphisms on the two-sphere [11][12][13][14][15][16], which gives rise to two infinite sets of flux-balance laws [8,11,14,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Thanks to junction conditions at spatial infinity [18], the generalized BMS group is a symmetry of the quantum gravity S-matrix, which gives rise to Ward identities that are identical to Weinberg' soft graviton theorem [33] and to the subleading soft graviton theorem [15,34].…”

“…To leading order when r → ∞ the metric (3.14) is defined by the so-called Bondi mass aspect m, angular momentum aspect N a and shear C ab (see e.g. [10,27,32]). These are functions of time u and the angles θ a .…”

“…As shown in [32], this quantity requires a prescription for α which is fixed to α = 1 in [14,20,24,28], α = 0 in [22,63] or α = 3 in [27]. Since the α-term gives instantaneous…”

“…Similarly there are corrections associated with the losses of linear momentum (or recoil) and the position of the center of mass, see e.g [32,53]…”

A note on dual gravitational charges

“…But a crucial question in this respect is whether there are dual contributions that contain radiative modes, and would impact the flux-balance laws of the standard BMS charges (see e.g. [40]).…”