Boundary Energy-Momentum Tensors for Asymptotically Flat Spacetimes

TL;DR

This paper develops a boundary energy-momentum tensor framework for 3D and 4D asymptotically flat spacetimes with Carroll geometry, linking it to Bondi mass loss and angular momentum, and explores Weyl invariance and boost anomalies.

Contribution

It introduces a boundary energy-momentum tensor for asymptotically flat spacetimes with Carroll geometry, connecting it to physical conservation laws and anomalies.

Findings

Boundary energy-momentum tensor defined with counterterms.

Diffeomorphism Ward identity matches Bondi mass and angular momentum loss.

Weyl invariance and boost anomalies identified in 3D and 4D.

Abstract

We consider 3D and 4D asymptotically flat spacetimes near future null infinity endowed with the most general allowed Carroll geometry. We define a boundary energy-momentum tensor by varying the on-shell action with respect to the Carroll metric data. This requires adding counterterms to the Einstein-Hilbert action. We show that, in 4D, the shear is on par with the Carroll metric data. Their combined response defines a boundary energy-momentum-news complex whose diffeomorphism Ward identity is equivalent to the Bondi mass and angular momentum loss equations. Weyl invariance leads to an identity for the trace of the energy-momentum tensor, and local Carroll boosts are anomalous in 3D and in 4D.