Equivalent Formulations of Carrollian Gravity: Curvature, Torsion, and non-gravitational theories

• Aliasghar Parvizi (School of Physics, IPM)

Carrollian geometry emerges as the ultra-relativistic limit of spacetime and has recently attracted considerable attention due to its appearance in flat-space holography, null hypersurface dynamics, BMS symmetries, and ultra-relativistic fluid dynamics. In this talk, I will first review the basic principles of Carrollian geometry and discuss its relevance in modern theoretical physics. I will then focus on recent developments in Carrollian gravity and present our recent work on equivalent formulations of Carrollian gravity within the class of metric-compatible connections. Inspired by the Geometrical Trinity of General Relativity, we show that the action of Magnetic Carrollian Gravity can be systematically exchanged for different torsional sectors. This leads to equivalent descriptions based on intrinsic, spatial, and temporal torsions. These formulations establish novel connections between Carrollian gravity, teleparallel-like geometries and non-gravitational theories.