Counting Components in the Lagrange Multiplier Formulation of Teleparallel Theories

TL;DR

This paper compares the Lagrange multiplier formulation of teleparallel theories, including f(T) gravity, with the pure frame approach, revealing their equivalence and implications for local Lorentz invariance and associated pathologies.

Contribution

It demonstrates the equivalence between the Lagrange multiplier and pure frame formulations of teleparallel theories, clarifying issues related to local Lorentz invariance in f(T) gravity.

Findings

The two formulations are dynamically equivalent.

Manifestly local Lorentz invariant f(T) theory may have pathologies.

Comparison clarifies the structure of teleparallel gravity theories.

Abstract

We investigate the Lagrange multiplier formulation of teleparallel theories, including f(T) gravity, in which the connection is not set to zero a priori and compare it with the pure frame theory. We show explicitly that the two formulations are equivalent, in the sense that the dynamical equations have the same content. One consequence is that the manifestly local Lorentz invariant f(T) theory cannot be expected to be free of pathologies, which were previously found to plague f(T) gravity formulated in the usual pure frame approach.