# On the covariance of teleparallel gravity theories

## TL;DR

This paper reviews teleparallel gravity theories, focusing on Lorentz symmetry issues and covariant formulations, and introduces a new form of $f(T)$ field equations to address these challenges.

## Contribution

It provides a comprehensive review of teleparallel gravity, discusses covariantization methods, and presents a novel form of $f(T)$ field equations.

## Key findings

- Analysis of Lorentz-breaking issues in pure-tetrad models
- Discussion of covariantization approaches for teleparallel theories
- Introduction of a new form of $f(T)$ field equations

## Abstract

The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models are discussed. A by-product is a new form of $f(T)$ field equations.