Towards the physical significance of the $(k^2+A)\|u\|$ metric

TL;DR

This paper explores a second order Kawaguchi metric function that extends the semi-classical spinning particle model to pseudo-Riemannian space-time, developing related variational equations.

Contribution

It introduces a new second order Kawaguchi metric function and derives the associated fourth order Euler-Poisson equations in pseudo-Riemannian geometry.

Findings

Generalizes flat space-time models to pseudo-Riemannian space-time

Develops the shape of variational Euler-Poisson equations in this context

Provides an example of the second order Kawaguchi metric function

Abstract

We offer an example of the second order Kawaguchi metric function the extremal flow of which generalizes the flat space-time model of the semi-classical spinning particle to the framework of the pseudo-Riemannian space-time. The general shape of the variational Euler-Poisson equation of the fourth order in the (pseudo-)Riemannian space is being developed too.