Generalizations of teleparallel gravity and local Lorentz symmetry

TL;DR

This paper investigates how modifications to teleparallel gravity affect local Lorentz symmetry, clarifying differences with general relativity and analyzing the viability of generalized theories like f(T).

Contribution

It provides a detailed analysis of local Lorentz invariance in teleparallel theories and offers a method to construct equivalent theories, highlighting issues in restoring symmetry in f(T) models.

Findings

Generic teleparallel modifications break local Lorentz invariance.

Restoring Lorentz symmetry in f(T) theories leads to inconsistent dynamics.

Explicit construction methods for teleparallel equivalents are provided.

Abstract

We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensible dynamics, even if one gives up teleparallelism.