The general relativity dynamics in the Eisenhart geometry
type: Item
instance of: scholarly article
title: The general relativity dynamics in the Eisenhart geometry
zbMATH Open document ID: 0952.83008
DOI: 10.1016/S0960-0779(98)00168-4
author: Marek Szydłowski
published in: Chaos, Solitons and Fractals
publication date: 2000-08-09T00:00:00Z
review text: The Eisenhart's principle is used as an alternative geometrical construction on minisuperspace. It is shown that this principle maps the trajectories of Hamiltonian systems into geodesic on certain extended configuration space. The Eisenhart geometry appears as the right way to desingularization of motion in the Jacobi metric. The author presents different methods of desingularization of the Jacobi metric through the isometric embedding into a flat space with the Lorentzian signature. The extension of the Fermat principle to the case of timelike trajectories is also studied. A theorem, which establishes one-to-one correspondence between trajectories of simple definite systems and trajectories of fictitious particles in spacetime with Eisenhart geometry, is proven. It is concluded that the geometrization according to Eisenhart's principle enables to build geometrical models of dynamics in different spaces: Euclidean, Riemannian, Weyl affine, Einstein-Cartan with torsion and Finsler spaces.
reviewed by: Gheorghe Zet
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 83C10
zbMATH DE Number: 1486538
zbMATH Keywords: minisuperspace
zbMATH Keywords: Eisenhart principle
zbMATH Keywords: nonsingular metric
zbMATH Keywords: timelike trajectory
zbMATH Keywords: isometric embedding
zbMATH Keywords: Lorentzian signature
zbMATH Keywords: Fermat principle
MaRDI profile type: Publication
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full work available at URL: s0960-0779(98)00168-4
OpenAlex ID: W2095261404
description: scientific article; zbMATH DE number 1486538