### Выдержка

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.

Язык оригинала | Английский |
---|---|

Номер статьи | 301 |

Журнал | European Physical Journal C |

Том | 79 |

Номер выпуска | 4 |

DOI | |

Состояние | Опубликовано - 1 апр 2019 |

### Отпечаток

### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Physics and Astronomy (miscellaneous)

### Цитировать

*European Physical Journal C*,

*79*(4), [301]. https://doi.org/10.1140/epjc/s10052-019-6812-6

**Eisenhart lift of 2-dimensional mechanics.** / Fordy, Allan P.; Galajinsky, Anton.

Результат исследований: Материалы для журнала › Статья

*European Physical Journal C*, том. 79, № 4, 301. https://doi.org/10.1140/epjc/s10052-019-6812-6

}

TY - JOUR

T1 - Eisenhart lift of 2-dimensional mechanics

AU - Fordy, Allan P.

AU - Galajinsky, Anton

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85063963460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063963460&partnerID=8YFLogxK

U2 - 10.1140/epjc/s10052-019-6812-6

DO - 10.1140/epjc/s10052-019-6812-6

M3 - Article

VL - 79

JO - European Physical Journal C

JF - European Physical Journal C

SN - 1434-6044

IS - 4

M1 - 301

ER -