Conservation law of super-Lorentz charges across spatial infinity
Abstract
Under assumptions compatible with generic gravitational scattering, the vacuum relativistic gravitational field is entirely determined at leading order in the large radius expansion at spatial infinity by its supermomentum, its dual supermomentum and its global supertranslation frame. At subleading order, the gravitational field is determined by three additional sets of charges: the super-Lorentz charges, the leading mixed tail/ peeling-breaking charges and the leading peeling-breaking charges. In this work we provide a proper-supertranslation-invariant definition of these charges in terms of asymptotic Bondi-Sachs fields as well as a corresponding proper supertranslation and logarithmic translation invariant definition of these charges in terms of Beig-Schmidt fields. Using the properties of homogeneous and inhomogeneous solutions to relevant wave equations over the boundary de Sitter spacetime at spatial infinity, we derive the conservation law of super-Lorentz charges between the future and past of spatial infinity. We obtain that the super-Lorentz aspects are non-locally defined from the Bondi-Sachs fields.
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BibTeX
@misc{compere2026conservation,
title = {{Conservation law of super-Lorentz charges across spatial infinity}},
author = {Geoffrey Compère and Sébastien Robert},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.26848},
eprint = {2606.26848},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26848},
}
RIS
TY - UNPB
TI - Conservation law of super-Lorentz charges across spatial infinity
AU - Geoffrey Compère
AU - Sébastien Robert
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2606.26848
UR - https://arxiv.org/abs/2606.26848
AB - Under assumptions compatible with generic gravitational scattering, the vacuum relativistic gravitational field is entirely determined at leading order in the large radius expansion at spatial infinity by its supermomentum, its dual supermomentum and its global supertranslation frame. At subleading order, the gravitational field is determined by three additional sets of charges: the super-Lorentz charges, the leading mixed tail/ peeling-breaking charges and the leading peeling-breaking charges. In this work we provide a proper-supertranslation-invariant definition of these charges in terms of asymptotic Bondi-Sachs fields as well as a corresponding proper supertranslation and logarithmic translation invariant definition of these charges in terms of Beig-Schmidt fields. Using the properties of homogeneous and inhomogeneous solutions to relevant wave equations over the boundary de Sitter spacetime at spatial infinity, we derive the conservation law of super-Lorentz charges between the future and past of spatial infinity. We obtain that the super-Lorentz aspects are non-locally defined from the Bondi-Sachs fields.
ER -