Symmetric Teleparallel Geometries

Abstract

In teleparallel gravity and, in particular, in $F(T)$ teleparallel gravity, there is a challenge in determining an appropriate (co-)frame and its corresponding spin connection to describe the geometry. Very often, the "proper" frame, the frame in which all inertial effects are absent, is not the simplest (e.g, diagonal) (co-)frame. The determination of the frame and its corresponding spin connection for $F(T)$ teleparallel gravity theories when there exist affine symmetries is of much interest. In this paper we present the general form of the coframe and its corresponding spin connection for teleparallel geometries which are invariant under a $G_6$ group of affine symmetries. The proper coframe and the corresponding $F(T)$ field equations are also shown for these Teleparallel Robertson Walker (TRW) geometries. Further, with the addition of an additional affine symmetry, it is possible to define a Teleparallel de Sitter (TdS) geometry.

arXiv comment15 pages

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Cited by in corpus (18)

• A frame based approach to computing symmetries with non-trivial isotropy groups
• Exploring the stability of $f(Q)$ cosmology near general relativity limit with different connections
• Generalized Teleparallel de Sitter geometries
• Spatial curvature in coincident gauge $f(Q)$ cosmology
• Teleparallel Robertson-Walker geometries and applications
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
• Cosmological solutions in teleparallel $F(T,B)$ gravity
• Spatially Homogeneous Teleparallel Gravity: Bianchi I
• Teleparallel Geometry with a Single Affine Symmetry
• Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames
• Scalar field source Teleparallel Robertson-Walker F(T)-gravity solutions
• Locally-homogeneous Riemann-Cartan geometries with the largest symmetry group
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• On black holes in teleparallel torsion theories of gravity
• Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions
• On black holes in new general relativity
• Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions
• Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions