Relativistic mechanics in a general setting

TL;DR

This paper develops a general framework for relativistic mechanics on arbitrary manifolds using jet spaces, introducing a generic Lagrangian and focusing on pseudo-Riemannian cases, broadening the theoretical foundation of relativistic physics.

Contribution

It formulates relativistic mechanics on arbitrary manifolds with jets and constructs a generic Lagrangian, extending the scope beyond traditional models.

Findings

Formulation of relativistic mechanics on arbitrary manifolds

Construction of a generic relativistic Lagrangian

Special consideration of pseudo-Riemannian manifolds

Abstract

Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly considered.