The covariant formulation of f(T) gravity

By Martin Krssák, Emmanuel N. Saridakis. 2015

376 citations recorded by the source corpus.

We show that the well-known problem of frame dependence and violation of local Lorentz invariance in the usual formulation of f(T) gravity is a consequence of neglecting the role of spin connection. We re-formulate f(T) gravity starting from, instead of the ‘pure tetrad’ teleparallel gravity, the covariant teleparallel gravity, using both the tetrad and the spin connection as dynamical variables, resulting in a fully covariant, consistent, and frame-independent version of f(T) gravity, which does not suffer from the notorious problems of the usual, pure tetrad, f(T) theory. We present the method to extract solutions for the most physically important cases, such as the Minkowski, the Friedmann–Robertson–Walker (FRW) and the spherically symmetric ones. We show that in covariant f(T) gravity we are allowed to use an arbitrary tetrad in an arbitrary coordinate system along with the corresponding spin connection, resulting always in the same physically relevant field equations.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/154d66f302b5e302b6dbbba1e1dac46d4d7a6b13

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Structure formation in f(T) gravity and a solution for H0 tension (2018, background): “However, a long term issue associated with f(T ) gravity is that it is not invariant under local Loretz tranformations [60], but probably such problem can also be solved if one introduces the spin connection along with the tetrad formalisms in f(T ) gravity [45].”
Cosmological perturbations in modified teleparallel gravity models (2018, background): “We will take the classical route of working with zero spin connection in f(T ) (pure tetrad formulation) because the covariantisation [19, 20], though important at the foundational level, introduces new variables without changing physical predictions which is impractical for our current purposes.”
Teleparallel theories of gravity: illuminating a fully invariant approach (2018, methodology): “It is interesting to note that in many highly symmetric situations, such as spherically symmetric spacetimes or isotropic cosmologies, the antisymmetric and symmetric parts of the field equations for the tetrad do decouple from each other [13, 131].”
On the covariance of teleparallel gravity theories (2017, positive): “As claimed in [20] and repeated in the review paper [17], the model can be Lorentz-covariantised by allowing for a spin-connection as a new variable because the spin-connection enters the teleparallel action only as a surface term.”
Dynamical systems applied to cosmology: Dark energy and modified gravity (2017, neutral): “Note that we are following the standard approach in teleparallel gravity where the spin connection is set to zero (see e.g. Maluf (2013)), rather than the covariant approach where the spin connection plays a more active role (Krššák & Saridakis, 2016).”