Setting the connection free in the Galilei and Carroll expansions of gravity

Fuente: arXiv
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Autores principales: Musaeus, Jørgen, Obers, Niels A., Oling, Gerben
Formato: Preprint
Publicado: 2023
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author Musaeus, Jørgen
Obers, Niels A.
Oling, Gerben
author_facet Musaeus, Jørgen
Obers, Niels A.
Oling, Gerben
contents We obtain a Palatini-type formulation for the Galilei and Carroll expansions of general relativity, where the connection is promoted to a variable. Known versions of these large and small speed of light expansions are derived from the Einstein-Hilbert action and involve dynamical Newton-Cartan or Carroll geometry, along with additional gauge fields at subleading orders. The corresponding Palatini actions that we obtain in this paper are derived from an appropriate expansion of the Einstein-Palatini action, and the connection variable reduces to the Galilei- or Carroll-adapted connection on shell. In particular, we present the Palatini form for the next-to-leading order Galilean action and recover the known equations of motion. We also compute the leading-order Palatini-type action for the Carrollian case and show that, while it depends on the connection variable, it reduces on shell to the known action of electric Carroll gravity, which only depends on extrinsic curvature.
format Preprint
id arxiv_https___arxiv_org_abs_2312_13924
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Setting the connection free in the Galilei and Carroll expansions of gravity
Musaeus, Jørgen
Obers, Niels A.
Oling, Gerben
High Energy Physics - Theory
General Relativity and Quantum Cosmology
We obtain a Palatini-type formulation for the Galilei and Carroll expansions of general relativity, where the connection is promoted to a variable. Known versions of these large and small speed of light expansions are derived from the Einstein-Hilbert action and involve dynamical Newton-Cartan or Carroll geometry, along with additional gauge fields at subleading orders. The corresponding Palatini actions that we obtain in this paper are derived from an appropriate expansion of the Einstein-Palatini action, and the connection variable reduces to the Galilei- or Carroll-adapted connection on shell. In particular, we present the Palatini form for the next-to-leading order Galilean action and recover the known equations of motion. We also compute the leading-order Palatini-type action for the Carrollian case and show that, while it depends on the connection variable, it reduces on shell to the known action of electric Carroll gravity, which only depends on extrinsic curvature.
title Setting the connection free in the Galilei and Carroll expansions of gravity
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2312.13924