The Poincar\'e and BMS flux-balance laws with application to binary systems

TL;DR

This paper comprehensively derives flux-balance laws for all BMS charges in asymptotically flat spacetimes, linking them to gravitational wave memory effects and providing exact constraints on waveforms from binary black hole mergers.

Contribution

It presents the complete form of Poincaré and BMS flux-balance laws, including all relevant memory effects, in terms of radiative multipoles, and applies these laws to binary black hole systems.

Findings

Fluxes of energy, angular momentum, and super-angular momentum appear at 2.5PN.

Quadrupole supermomentum fluxes appear at 3PN.

Constraints on gravitational waveforms from BMS flux-balance laws.

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 Poincar\'e 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 Poincar\'e 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.