Geometric action for extended Bondi-Metzner-Sachs group in four dimensions

TL;DR

This paper develops a geometric action framework for the extended BMS4 group in four dimensions, linking Hamiltonian analysis, celestial holography, and asymptotic spacetime evolution.

Contribution

It introduces a field theory in 2+1 dimensions that realizes the extended BMS4 algebra through Poisson brackets and reproduces spacetime evolution equations.

Findings

Poisson bracket algebra matches extended BMS4 Lie algebra

Model includes classical operator product expansions

Reproduces evolution equations of non-radiative spacetimes

Abstract

The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS$_4$ generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS$_4$ Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. Furthermore, the model reproduces the evolution equations of non-radiative asymptotically flat spacetimes at null infinity.