Boundary Energy-Momentum Tensors for Asymptotically Flat Spacetimes
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.
Keywords
Cite
@article{arxiv.2505.05432,
title = {Boundary Energy-Momentum Tensors for Asymptotically Flat Spacetimes},
author = {Jelle Hartong and Emil Have and Vijay Nenmeli and Gerben Oling},
journal= {arXiv preprint arXiv:2505.05432},
year = {2025}
}
Comments
v2: citations added, typos fixed, missing term added to boost anomaly