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arXiv · 2512.14688

Torsional Carroll Gravity

P. Concha·N. Merino·L. Ravera·E. Rodríguez
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Abstract

The ultra-relativistic (Carrollian) regime of gravity has recently emerged as a fertile framework for exploring holography, non-Lorentzian symmetries, and geometric limit of General Relativity. In this letter, we establish the presence of a non-vanishing torsion within three-dimensional Carrollian gravity by constructing the Carrollian Mielke-Baekler (C-MB) gravity theory in its Chern-Simons formulation, obtained as the ultra-relativistic limit of the relativistic Mielke-Baekler model. The resulting C-MB theory features non-zero temporal torsion and curvature, together with spatial curvature, providing the most general three-dimensional Carrollian gravity model with these properties. Temporal torsion affects non-affinity of null generators and boundary dynamics. Several known ultra-relativistic gravity theories arise as particular limits of this framework, highlighting its unifying character.

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P. Concha, N. Merino, L. Ravera, E. Rodríguez. 2025-12-16. Torsional Carroll Gravity. https://doi.org/10.1103/9dcc-6vsh

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