Two-point boundary value problems in relativistic dynamics
type: Item
instance of: scholarly article
title: Two-point boundary value problems in relativistic dynamics
zbMATH Open document ID: 0884.58036
DOI: 10.1007/BF02308544
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: The paper starts with an action functional for the motion of a test particle in a Lorentzian manifold \((M,g)\), composed of a velocity term, a Maxwell field term, and a Newton potential term. An extremal curve is taken as the projection of a geodesic in a Kaluza-Klein manifold, which is a bundle over \(M\) and is equipped with a bundle metric composed of \(g\), a Maxwell potential, and the Newton potential. It is shown that there exists an extremal with prescribed boundary points if \((M,g)\) is globally hyperbolic and some other mild conditions are satisfied. The proof uses arguments of variational calculus, homotopy, cohomology, and the theory of causal structures.
Mathematics Subject Classification ID: 58E50
Mathematics Subject Classification ID: 83C10
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1028525
zbMATH Keywords: test particle motion
zbMATH Keywords: boundary value problem
zbMATH Keywords: Lorentzian manifold
author: E. I. Yakovlev
reviewed by: Rainer Schimming
MaRDI profile type: Publication
cites work: Q3197019
cites work: Q4748786
full work available at URL: https://doi.org/10.1007/bf02308544
OpenAlex ID: W1971753742
description: scientific article; zbMATH DE number 1028525