Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions

Abstract

The f(T) gravity is nowadays being widely used for cosmological model building, as well as for constructing spherically symmetric solutions. In its classical pure tetrad formulation it violates the local Lorentz symmetry in the space of tetrads. By using an appropriate spin connection it can be brought to a formally Lorentz invariant shape. However, despite some mathematical elegance obtained and new options of looking for non-standard couplings to matter probably made possible, it is fully equivalent in itself to the initial formulation. It seems that this fact, that the covariantisation does not in principle change anything, is not understood well by the community. Therefore we give a pedagogical introduction to these topics. And, on top of that, we show that obtaining the explicit equations for spherically symmetric solutions in f(T) gravity is not very difficult computationally and can be easily done even without any computer at hand.

13 pages; some more explanations added

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• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Geometry and covariance of symmetric teleparallel theories of gravity
• Thick accretion disk configurations in the Born-Infeld teleparallel 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
• The geometrical meaning of the Weitzenböck connection
• Static spherically symmetric perfect fluid solutions in teleparallel F(T) gravity
• The amplification of cosmological magnetic fields in Extended $f(T,B)$ Teleparallel Gravity
• Solving Tolman-Oppenheimer-Volkoff equations in $f(T)$ gravity: a novel approach
• Kantowski-Sachs spherically symmetric solutions in teleparallel $F(T)$ gravity
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• Static spherically symmetric solutions in New General Relativity
• Resolving FLRW cosmology through effective equations of state in $f(T)$ gravity
• Gravitational Waves in New General Relativity
• Teleparallel Geometry with a Single Affine Symmetry
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Degrees of Freedom in modified Teleparallel Gravity
• Teleparallel dark energy in a nonflat universe
• Probing symmetric teleparallel gravity in the early universe
• Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint
• Geometry of teleparallel theories
• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• Scalar Field Static Spherically Symmetric Solutions in Teleparallel $F(T)$ Gravity
• Local symmetries in $f(T)$-like models: lessons from 2D
• More on Bianchi I spacetimes and f(T) gravity
• Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions
• Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions