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

TL;DR

This paper provides a complete, first-principles derivation of all Poincaré and proper BMS flux-balance laws for asymptotically flat spacetimes within Bondi gauge, connecting them to the three memory effects defined by the Bondi shear. It expresses the exact laws in terms of radiative STF multipoles, derives their post-Newtonian expansions, and shows how these fluxes constrain the evolution of source parameters in compact binaries, including the initial and final Kerr states in arbitrary Lorentz and supertranslation frames. The work clarifies ambiguities in angular-momentum and center-of-mass definitions, introduces covariant and intrinsic Lorentz charges, and demonstrates how the BMS laws provide nontrivial consistency relations for gravitational-wave waveforms and radiation-reaction effects. By applying the framework to binary Kerr systems, it yields explicit global conservation statements and memory predictions that can guide numerical relativity and GW data analysis. Overall, the results offer a rigorous bridge between asymptotic symmetry structures and observable GW signatures, including spin, displacement, and center-of-mass memories.

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.