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

References in corpus (7)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The teleparallel equivalent of general relativity
• Finsler and Lagrange Geometries in Einstein and String Gravity
• Conformal Invariant Teleparallel Cosmology
• Teleparallel gauge theory of gravity
• On Gravitational Energy in Conformal Teleparallel Gravity
• An Extension of Teleparallelism and the Geometrization of the Electromagnetic Field

Cited by in corpus (2)

• Noether charge and black hole entropy in teleparallel gravity
• Teleparallel theory as a gauge theory of translations: comments and issues