Symmetry group at future null infinity III: Gravitational theory

TL;DR

This paper develops a detailed analysis of the gravitational symmetry algebra at future null infinity in asymptotically flat spacetimes, including supertranslations, superrotations, and duality operators, with implications for boundary field theories.

Contribution

It constructs a closed symmetry algebra of gravitational generators at null infinity, incorporating a generalized duality operator, and relates these to boundary Hamiltonians and BMS fluxes.

Findings

Constructed Poincaré flux operators at null infinity.

Established a closed algebra including supertranslations, superrotations, and duality.

Linked generators to boundary Hamiltonians and BMS fluxes.

Abstract

We reduce the gravitational theory in an asymptotically flat spacetime to future null infinity. We compute the Poincar\'e flux operators at future null infinity and construct the supertranslation and superrotation generators. The generators are shown to form a closed symmetry algebra by including a generalized gravitational duality operator. We could regard all the generators as the Hamiltonians with respect to the symmetry transformation in the boundary field theory. Our construction of the generators may relate to the BMS fluxes defined in the literature by adding counterterms to the Bondi mass and angular momentum aspects.