Non-geodesic Motion in General Relativity and Thermodynamics

TL;DR

This paper explores the extension of a previously established link between geodesic-based metrics in General Relativity and the Dirac Equation to arbitrary curves, also examining a mass-temperature relationship for scalar fields.

Contribution

It extends the connection between linearized metrics and quantum mechanics from geodesics to arbitrary curves, and investigates a mass-temperature relationship for scalar fields.

Findings

Relationship between mass and temperature for scalar fields.

Extension of metric-Dirac equation link to arbitrary curves.

New insights into non-geodesic motion in GR and thermodynamics.

Abstract

In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves is investigated. In the case of scalar fields, a relationship between mass and temperature is also worked out.