Premetric equivalent of general relativity: Teleparallelism

TL;DR

This paper develops a premetric formulation of general relativity using teleparallelism, separating topological and metric-dependent aspects, and enabling extensions to diverse spacetime geometries.

Contribution

It introduces a premetric approach to GR via teleparallelism, formulating metric-free topological equations and constitutive laws, and shows equivalence to standard GR under local Lorentz invariance.

Findings

Premetric formulation of GR achieved through teleparallelism.

Formulation of metric-free topological field equations.

Establishment of a full equivalence to GR with Lorentz invariance.

Abstract

In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely topological field equation from the metric-dependent constitutive law. We show here that GR allows for a premetric formulation, too. For this purpose, we apply the teleparallel approach of gravity, which represents GR as a gauge theory based on the translation group. We formulate the metric-free topological field equation and a general linear constitutive law between the basic field variables. The requirement of local Lorentz invariance turns the model into a full equivalent of GR. Our approach opens a way for a natural extension of GR to diverse geometrical structures of spacetime.