Lorentz symmetries and primary constraints in covariant teleparallel gravity

TL;DR

This paper investigates the role of Lorentz symmetries and primary constraints in covariant teleparallel gravity, highlighting issues of local Lorentz symmetry breaking in the Hamiltonian formulation of modified theories.

Contribution

It analyzes the primary constraints and their algebra in covariant $f(T)$ gravity, revealing persistent Lorentz symmetry breaking issues.

Findings

Primary constraints are identified and their algebra computed.

Lorentz symmetry breaking persists in covariant $f(T)$ gravity.

The Hamiltonian formulation exposes underlying symmetry issues.

Abstract

In this article we explore local Lorentz transformations in theories of gravity based on the teleparallel formalism. For the teleparallel equivalent of general relativity (TEGR), the spin connection plays no role in the equations of motion, and therefore it is possible to simply put it equal to zero with no change in physical quantities, and then the theory is formulated purely in terms of the tetrad field which can be freely chosen in any way. In nonlinear modifications of TEGR, this is a more intricate issue, and vanishing spin connection is then the Weitzenb\"{o}ck gauge choice which imposes restrictions on the choice of tetrad. This has led to considering the so-called covariant formulation of $f(T)$ gravity. We examine the primary constraints arising when passing to the Hamiltonian framework, and compute their algebra. We show that the problems of local Lorentz symmetry breaking still appear in this formulation, even if in a different disguise.