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arXiv · 2606.26848

Conservation law of super-Lorentz charges across spatial infinity

Geoffrey Compère·Sébastien Robert
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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 tail charges and the leading peeling-breaking charges. In this work we provide a supertranslation-invariant definition of these charges in terms of asymptotic Bondi-Sachs fields as well as a corresponding 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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Geoffrey Compère, Sébastien Robert. 2026-06-25. Conservation law of super-Lorentz charges across spatial infinity. https://arxiv.org/abs/2606.26848

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