PreprintCC BY 4.0arXiv
From Holst to Carroll Gravity, a Hamiltonian point of view
Abstract
The Carrollian regime of gravity provides a useful ultrarelativistic framework for studying asymptotically flat spacetimes, horizon dynamics, and condensed matter systems. In this paper, we present a comprehensive Hamiltonian analysis of the most general Carroll-invariant Lagrangian that can be derived from the Holst action. To guide the analysis, Cartan geometry tools are used. We identify the full constraint structure of the theory, characterize its gauge symmetries, obtain the explicit form of the Hamiltonian vector fields and introduce Ashtekar-like variables for the magnetic Carrollian regime. We also discuss in detail an analog of the time gauge employed in the Hamiltonian analysis of the Holst action for general relativity.
Versions
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BibTeX
@misc{barbero2026from,
title = {{From Holst to Carroll Gravity, a Hamiltonian point of view}},
author = {J. Fernando Barbero G and Juan Margalef-Bentabol and Valle Varo and Eduardo J. S. Villaseñor},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.26799},
eprint = {2606.26799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26799},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Holst to Carroll Gravity, a Hamiltonian point of view
AU - J. Fernando Barbero G
AU - Juan Margalef-Bentabol
AU - Valle Varo
AU - Eduardo J. S. Villaseñor
PY - 2026
DA - 2026/06/25
PB - arXiv
DO - 10.48550/arxiv.2606.26799
UR - https://arxiv.org/abs/2606.26799
AB - The Carrollian regime of gravity provides a useful ultrarelativistic framework for studying asymptotically flat spacetimes, horizon dynamics, and condensed matter systems. In this paper, we present a comprehensive Hamiltonian analysis of the most general Carroll-invariant Lagrangian that can be derived from the Holst action. To guide the analysis, Cartan geometry tools are used. We identify the full constraint structure of the theory, characterize its gauge symmetries, obtain the explicit form of the Hamiltonian vector fields and introduce Ashtekar-like variables for the magnetic Carrollian regime. We also discuss in detail an analog of the time gauge employed in the Hamiltonian analysis of the Holst action for general relativity.
ER -