Lorentz symmetries and primary constraints in covariant teleparallel gravity

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 Weitzenböck 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.

19 pages, no figures, comments welcome

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• Teleparallel Gravity: From Theory to Cosmology
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Geometry and covariance of symmetric teleparallel theories of gravity
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• On spherically symmetric vacuum solutions and horizons in covariant $f(T)$ gravity theory
• Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density
• On the role of constraints and degrees of freedom in the Hamiltonian formalism
• A geometric view on local Lorentz transformations in teleparallel gravity
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• Teleparallel bigravity
• Inhomogeneous solutions in $f(T,B)$ gravity
• The generalization of the ADM gravitational energy-momentum
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity