Boundary Energy-Momentum Tensors for Asymptotically Flat Spacetimes

Jelle Hartong; Emil Have; Vijay Nenmeli; Gerben Oling

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arXiv · 2505.05432

Boundary Energy-Momentum Tensors for Asymptotically Flat Spacetimes

Jelle Hartong·Emil Have·Vijay Nenmeli·Gerben Oling

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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.

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Jelle Hartong, Emil Have, Vijay Nenmeli, Gerben Oling. 2025-06-05. Boundary Energy-Momentum Tensors for Asymptotically Flat Spacetimes. https://arxiv.org/abs/2505.05432

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