Premetric teleparallel theory of gravity and its local and linear constitutive law

TL;DR

This paper develops a premetric teleparallel gravity framework with a focus on local and linear constitutive laws, analyzing its structure, tensor decomposition, and wave propagation characteristics, including connections to Einstein's general relativity.

Contribution

It introduces a comprehensive structure of teleparallel gravity using a Tonti diagram and tensor decomposition, incorporating axion and skewon effects, and explores wave propagation in this framework.

Findings

Derived the structure of TG via Tonti diagram.

Constructed general constitutive tensors including axion and skewon components.

Analyzed wave propagation for massless spins 0, 1, 2, relating to Einstein's GR.

Abstract

We continue to investigate the premetric teleparallel theory of gravity (TG) with the coframe (tetrad) as gravitational potential. We start from the field equations and a local and linear constitutive law. We create a Tonti diagram of TG in order to disclose the structure of TG. Subsequently we irreducibly decompose the 6th order constitutive tensor under the linear group. Moreover, we construct the most general constitutive tensors from the metric and the totally antisymmetric Levi-Civita symbol, and we demonstrate that they encompass nontrivial axion and skewon type pieces. Using these tools, we derive for TG in the geometric-optics approximation propagating massless spin 0, 1, and 2 waves, including the special case of Einstein's general relativity.