Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions

TL;DR

This paper develops a framework for defining conserved stress tensor and current at null infinity in 3D flat spacetimes, linking boundary geometry to holography and fluid dynamics, and deriving a Schwarzian action for boundary reparametrizations.

Contribution

It introduces a novel intrinsic conserved stress tensor and current at null infinity in 3D, connecting boundary Carrollian geometry to flat holography and fluid/gravity correspondence.

Findings

Reproduces Bondi-mass and angular momentum conservation equations.

Establishes a flat holography framework with a boundary Schwarzian action.

Links boundary reparametrizations to a Schwarzian dynamics at null infinity.

Abstract

We develop the framework that reveals the intrinsic conserved stress tensor and current associated with the null infinity of a three-dimensional ($3d$) asymptotically flat spacetime. These are, respectively, canonical conjugates of degenerate metric and Ehresmann connection of the boundary Carrollian geometry. Their conservation reproduces the Bondi-mass and angular momentum conservation equations if the asymptotic boundary is endowed with a torsional affine connection that we specify. Our analysis and results shed further light on the $3d$ flat holography; the stress tensor and current give rise to an asymptotically flat fluid/gravity correspondence. The requirement of a well-defined $3d$ action principle yields Schwarzian action at null infinity governing the dynamics induced by reparametrizations over the celestial circle, in accord with the codimension $2$ holography of $3d$ flat spacetimes.