Eisenhart lift of 2-dimensional mechanics

Eisenhart lift of 2-dimensional mechanics

Bibliographic Details
Parent link:The European Physical Journal C: Scientific Journal
Vol. 79, iss. 4.— 2019.— [301, 11 р.,]
Main Author: Fordy A. P.
Corporate Author: Национальный исследовательский Томский политехнический университет Исследовательская школа физики высокоэнергетических процессов
Other Authors: Galajinsky A. V. Anton Vladimirovich
Summary:Title screen
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) -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.
Режим доступа: по договору с организацией-держателем ресурса
Language:English
Published: 2019
Subjects:
электронный ресурс
труды учёных ТПУ
лифт Эйзенхарта
двухмерное проектирование
Online Access:https://doi.org/10.1140/epjc/s10052-019-6812-6
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=660159

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