Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry

Abstract

A brief discussion is made about the relevance of surface terms in the Lagrangian and Hamiltonian formulations of theories of gravity. These surface terms play an important role in the variation of the action integral and in the definition of field quantities such as the gravitational energy-momentum. Then we point out several inconsistencies of a recently proposed formulation of teleparallel theories of gravity with local Lorentz symmetry.

18 pages, no figures, several references added. In addition to previous criticisms, we show that there is an inconsistency stemming from the definition of proper frames in the context of teleparallel theories with a flat spin connection. Published in the Classical and Quantum Gravity

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• Modified gravity: a unified approach
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density
• The geometrical meaning of the Weitzenböck connection
• A geometric view on local Lorentz transformations in teleparallel gravity
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• The generalization of the ADM gravitational energy-momentum
• On the gravitational energy problem and the energy of photons
• The meaning of torsion in teleparallel theories
• Energy of Gravitational Radiation and the Background Energy of the Space-Time
• Phase space structure of symmetric teleparallel theory of gravity
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• Einstein gravity from the Einstein action: Counterterms and covariance
• Kerr-Schild metrics in teleparallel gravity
• On Gravitational Stefan-Boltzmann Law and Casimir Effect in FRW Universe