Carrollian-holographic Derivation of Gravitational Flux-Balance Laws
Adrien Fiorucci, Simon Pekar, P. Marios Petropoulos, Matthieu Vilatte
TL;DR
This work develops a Carrollian boundary framework for asymptotically flat gravity and derives the BMS flux-balance evolution equations for the mass aspect $M$ and angular momentum aspect $N_a$ from boundary symmetries, given a minimal holographic dictionary. It introduces hypermomenta conjugate to radiative boundary data and identifies their bulk counterparts with gravitational fields such as the Bondi shear $C_{ab}$ and Bondi news $N_{ab}$, linking boundary and bulk data. By enforcing Carroll boost, rotation, Weyl, and diffeomorphism invariance, the authors obtain flux-balance laws that reproduce the Bondi fluxes for $M$ and $N_a$. The results provide a purely boundary-based, intrinsic derivation and a Carrollian perspective on flat-space holography, paving the way for a holographic dual description of radiative data.
Abstract
We demonstrate that the BMS evolution equations for the mass and angular momentum aspects in asymptotically flat Einstein gravity follow from local Carroll, Weyl, and diffeomorphism invariance at the null conformal boundary, upon providing a minimalistic holographic dictionary as the sole input from the bulk. This result is a significant step in the quest for a flat-space holographic correspondence and offers a geometric implementation of the radiative degrees of freedom that source the boundary theory in the presence of bulk gravitational waves.