A small guide to variations in teleparallel gauge theories of gravity and the Kaniel-Itin model

TL;DR

This paper examines variations in teleparallel gauge theories of gravity, focusing on the Kaniel-Itin model, and clarifies the mathematical properties of coframe variations crucial for understanding its solutions.

Contribution

It provides a detailed analysis of the variation of the coframe in teleparallel gravity, correcting previous literature and evaluating the Kaniel-Itin model's properties.

Findings

Derived a master formula for the coframe variation commutator.

Corrected mistakes in existing literature regarding coframe variations.

Discussed the implications of the Kaniel-Itin model for teleparallel gravity.

Abstract

Recently Kaniel & Itin proposed a gravitational model with the wave type equation [\square+\lambda(x)]\vartheta^\alpha=0 as vacuum field equation, where \vartheta^\alpha denotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corresponding mistakes in the literature. Then we turn to a detailed discussion of the Kaniel-Itin model.