Fordy, AP orcid.org/0000-0002-2523-0262 and Galajinsky, A (2019) Eisenhart lift of 2-dimensional mechanics. The European Physical Journal C - Particles and Fields, 79. 301. ISSN 1434-6044
Abstract
The Eisenhart lift is a variant of geometrization of classical mechanics with d degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on (d+2)
(d+2)
-dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of 2-dimensional mechanics on curved background is studied. The corresponding 4-dimensional metric is governed by two scalar functions which are just the conformal factor and the potential of the original dynamical system. We derive a conformal symmetry and a corresponding quadratic integral, associated with the Eisenhart lift. The energy–momentum tensor is constructed which, along with the metric, provides a solution to the Einstein equations. Uplifts of 2-dimensional superintegrable models are discussed with a particular emphasis on the issue of hidden symmetries. It is shown that for the 2-dimensional Darboux–Koenigs metrics, only type I can result in Eisenhart lifts which satisfy the weak energy condition. However, some physically viable metrics with hidden symmetries are presented.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Apr 2019 13:35 |
Last Modified: | 25 Jun 2023 21:46 |
Status: | Published |
Publisher: | Springer Berlin Heidelberg |
Identification Number: | 10.1140/epjc/s10052-019-6812-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144414 |