The Geometry of Gravitational Radiation
Abstract
We consider 4-dimensional asymptotically flat vacuum spacetimes near future null infinity endowed with the most general allowable Carroll geometry. We show that the near-boundary radial expansion (to a certain order) can be organised in terms of connections that can be obtained by gauging the conformal Carroll algebra. The only non-vanishing curvatures in this gauging procedure are those that are associated with the special conformal generators and we will refer to these as the K-curvatures. The vanishing of these K-curvatures defines an asymptotic vacuum spacetime and we use this to construct a boundary (i.e. Carroll) covariant expression for the vacuum (soft) shear in terms of two boundary Carroll scalar fields. The K-curvatures transform in a hierarchical fashion into one another under Carroll boosts. This leads to a classification of 4 types of spacetimes: vacuum, strongly and weakly non-radiative, and radiative spacetimes. It is shown that the K-curvatures correspond to 5 of the 10 Weyl tensor components at leading order in their 1/r expansion. We furthermore observe that one of the K-curvatures is equal to the recently found Carroll boost anomaly. Finally, we show that the Bondi loss equations for the boundary energy-momentum-news complex can be cast into a form involving another energy-momentum tensor with vanishing energy flux that is traceless and whose non-conservation is entirely captured by the K-curvatures. The BMS currents can be obtained by contracting this latter energy-momentum tensor with a Carroll conformal Killing vector.
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BibTeX
@misc{hartong2026geometry,
title = {{The Geometry of Gravitational Radiation}},
author = {Jelle Hartong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09954},
eprint = {2609.09954},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09954},
}
RIS
TY - UNPB
TI - The Geometry of Gravitational Radiation
AU - Jelle Hartong
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09954
UR - https://arxiv.org/abs/2609.09954
AB - We consider 4-dimensional asymptotically flat vacuum spacetimes near future null infinity endowed with the most general allowable Carroll geometry. We show that the near-boundary radial expansion (to a certain order) can be organised in terms of connections that can be obtained by gauging the conformal Carroll algebra. The only non-vanishing curvatures in this gauging procedure are those that are associated with the special conformal generators and we will refer to these as the K-curvatures. The vanishing of these K-curvatures defines an asymptotic vacuum spacetime and we use this to construct a boundary (i.e. Carroll) covariant expression for the vacuum (soft) shear in terms of two boundary Carroll scalar fields. The K-curvatures transform in a hierarchical fashion into one another under Carroll boosts. This leads to a classification of 4 types of spacetimes: vacuum, strongly and weakly non-radiative, and radiative spacetimes. It is shown that the K-curvatures correspond to 5 of the 10 Weyl tensor components at leading order in their 1/r expansion. We furthermore observe that one of the K-curvatures is equal to the recently found Carroll boost anomaly. Finally, we show that the Bondi loss equations for the boundary energy-momentum-news complex can be cast into a form involving another energy-momentum tensor with vanishing energy flux that is traceless and whose non-conservation is entirely captured by the K-curvatures. The BMS currents can be obtained by contracting this latter energy-momentum tensor with a Carroll conformal Killing vector.
ER -