## SciPost Submission Page

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

### by Geoffrey Compère, Roberto Oliveri, Ali Seraj

### Submission summary

As Contributors: | Geoffrey Compère · Roberto Oliveri · Ali Seraj |

Preprint link: | scipost_202002_00002v1 |

Date submitted: | 2020-02-17 |

Submitted by: | Oliveri, Roberto |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Gravitation, Cosmology and Astroparticle Physics |

Approach: | Theoretical |

### 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.