Conformal Teleparallel Theories and Weyl Geometry

Abstract

Despite the fact that General Relativity (GR) has been very successful, many alternative theories of gravity have attracted the attention of a significant number of theoretical physicists. Among these theories, we have theories with conformal symmetry. Here, the use of Weyl geometry to deal with conformal teleparallel gravity is reviewed in great detail. As an application, a model that can be set to be equivalent to the Teleparallel Equivalent of General Relativity (TEGR) and is invariant under diffeomorphisms, local Lorentz transformations (LLT) and Weyl transformations (WT) is created. Some $pp$-wave, spherically symmetric and cosmological solutions are obtained. It turns out that the class of possibles solutions is wider than that of TEGR. In addition, the total and the gravitational energies of the universe are calculated and analyzed.

42 pages and 4 figures

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Cited by in corpus (11)

• Noether charge and black hole entropy in teleparallel gravity
• Nonmetricity theories and aspects of gauge symmetry
• Teleparallel theory as a gauge theory of translations: comments and issues
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Scale-invariant cosmology in de Sitter gauge theory
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Teleparallel gravity as a gauge theory: coupling to matter with Cartan connection
• On the gravitational energy problem and the energy of photons
• Entanglement production in Einstein-Cartan theory
• Cartan approach to Teleparallel Equivalent to General Relativity: a review
• The meaning of torsion in teleparallel theories