Carroll-Cotton Tensors and Gravitational Radiation at Null Infinity
Abstract
We provide a first-principles definition of Cotton tensors on conformal Carroll geometries by gauging the conformal Carroll algebra. On the mathematical side, this analysis yields a conformally covariant object designed to quantify deviations from conformal flatness in Carrollian geometries. On the physical side, it offers a powerful geometric tool to describe gravitational radiative degrees of freedom at the conformal boundary of four-dimensional asymptotically flat spacetimes. Unlike the Bondi news, whose fully-covariant definition requires amendment by supplementary data that we identify with the Geroch tensor, the Carroll--Cotton tensors offer the natural geometric objects to quantify deviations from stationarity due to the emission of gravitational waves.
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BibTeX
@misc{fiorucci2026carrollcotton,
title = {{Carroll-Cotton Tensors and Gravitational Radiation at Null Infinity}},
author = {Adrien Fiorucci and Simon Pekar and P. Marios Petropoulos and Matthieu Vilatte},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.28741},
eprint = {2608.28741},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05742627v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Carroll-Cotton Tensors and Gravitational Radiation at Null Infinity
AU - Adrien Fiorucci
AU - Simon Pekar
AU - P. Marios Petropoulos
AU - Matthieu Vilatte
PY - 2026
DA - 2026/09/08
PB - HAL
DO - 10.48550/arxiv.2608.28741
UR - https://hal.science/hal-05742627v1
AB - We provide a first-principles definition of Cotton tensors on conformal Carroll geometries by gauging the conformal Carroll algebra. On the mathematical side, this analysis yields a conformally covariant object designed to quantify deviations from conformal flatness in Carrollian geometries. On the physical side, it offers a powerful geometric tool to describe gravitational radiative degrees of freedom at the conformal boundary of four-dimensional asymptotically flat spacetimes. Unlike the Bondi news, whose fully-covariant definition requires amendment by supplementary data that we identify with the Geroch tensor, the Carroll--Cotton tensors offer the natural geometric objects to quantify deviations from stationarity due to the emission of gravitational waves.
ER -