Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor

TL;DR

This paper introduces a nonholonomic mapping principle that extends Einstein's equivalence principle to spacetimes with curvature and torsion, leading to a new action principle and a modified energy-momentum conservation law.

Contribution

It presents a novel geometric framework for classical mechanics in curved and torsioned spacetimes, including a new covariant conservation law for energy-momentum.

Findings

Derivation of a new equation of motion with torsion force

Introduction of a covariant conservation law for energy-momentum in torsioned spacetime

Identification of autoparallel trajectories as inertia manifestations

Abstract

The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. An important consequence is a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force changes geodesic into autoparallel trajectories, which are a direct manifestation of inertia. The geometric origin of the torsion force is a closure failure of parallelograms. The torsion force changes the covariant conservation law of the energy-momentum tensor whose new form is derived.