Torsional Carroll Gravity

TL;DR

This paper introduces a new three-dimensional Carrollian gravity model with non-zero torsion, derived as an ultra-relativistic limit of a relativistic theory, unifying various ultra-relativistic gravity theories and impacting boundary dynamics.

Contribution

It constructs the first comprehensive Carrollian gravity model with torsion using a Chern-Simons formulation, extending the understanding of ultra-relativistic gravitational theories.

Findings

Presence of non-zero temporal torsion and curvature in the model

Unification of several known ultra-relativistic gravity theories as special cases

Impact of temporal torsion on boundary dynamics and null generator non-affinity

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.