{"paper":{"title":"The Geometry of Gravitational Radiation","arxiv_id":"2609.09954","primary_cat":"hep-th","submitted_at":"2026-09-09T09:44:40+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.67,"id":"s0","own":true,"role":"background","text":"We consider 4-dimensional asymptotically flat vacuum spacetimes near future null infinity endowed with the most general allowable Carroll geometry.","hedge":{"p":0.65,"label":"asserted"},"own_p":0.54,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.66,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.67,"limitation":0.0,"future_work":0.0,"contribution":0.32,"interpretation":0.0}},{"i":1,"p":0.48,"id":"s1","own":true,"role":"result","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.2,"quantitative":false,"quantitative_p":0.21,"role_probabilities":{"gap":0.0,"method":0.09,"result":0.48,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.43,"interpretation":0.0}},{"i":2,"p":0.74,"id":"s2","own":true,"role":"result","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.8,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.26,"role_probabilities":{"gap":0.0,"method":0.12,"result":0.74,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.01}},{"i":3,"p":0.53,"id":"s3","own":true,"role":"result","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.3,"quantitative":true,"quantitative_p":0.53,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.53,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.42,"interpretation":0.0}},{"i":4,"p":0.98,"id":"s4","own":true,"role":"result","text":"The $K$-curvatures transform in a hierarchical fashion into one another under Carroll boosts.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.74,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.01}},{"i":5,"p":0.95,"id":"s5","own":true,"role":"result","text":"This leads to a classification of 4 types of spacetimes: vacuum, strongly and weakly non-radiative, and radiative spacetimes.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.18,"quantitative":true,"quantitative_p":0.92,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.95,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.02}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"result","text":"It is shown that the $K$-curvatures correspond to 5 of the 10 Weyl tensor components at leading order in their $1/r$ expansion.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.11,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":7,"p":0.98,"id":"s7","own":true,"role":"result","text":"We furthermore observe that one of the $K$-curvatures is equal to the recently found Carroll boost anomaly.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.72,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.49,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.01}},{"i":8,"p":0.86,"id":"s8","own":true,"role":"result","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.18,"quantitative":false,"quantitative_p":0.16,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.86,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.0}},{"i":9,"p":0.89,"id":"s9","own":true,"role":"result","text":"The BMS currents can be obtained by contracting this 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