Variationality with second derivatives, relativistic uniform acceleration, and the 'spin'-curvature interaction in two-dimensional space-time

TL;DR

This paper introduces a variational approach to geodesic circles in 2D Riemannian manifolds, exploring their connection to relativistic acceleration and spin-curvature interactions.

Contribution

It presents a novel variational formulation for geodesic circles and investigates their relation to relativistic acceleration and spin-curvature effects in two-dimensional space-time.

Findings

Derived a variational formulation for geodesic circles

Linked geodesic circles to uniform relativistic acceleration

Explored spin-curvature interaction in 2D space-time

Abstract

A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.