Good and bad tetrads in f(T) gravity

Abstract

We investigate the importance of choosing good tetrads for the study of the field equations of $f(T)$ gravity. It is well known that this theory is not invariant under local Lorentz transformations, and therefore the choice of tetrad plays a crucial role in such models. Different tetrads will lead to different field equations which in turn have different solutions. We suggest to speak of a good tetrad if it imposes no restrictions on the form of $f(T)$. Employing local rotations, we construct good tetrads in the context of homogeneity and isotropy, and spherical symmetry, where we show how to find Schwarzschild-de Sitter solutions in vacuum. Our principal approach should be applicable to other symmetries as well.

25 pages

References in corpus (26)

• Modified teleparallel gravity: inflation without inflaton
• On Born-Infeld Gravity in Weitzenbock spacetime
• Cosmological perturbations in f(T) gravity
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Observational constraints on $f(T)$ theory
• f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis
• The Newtonian Limit of F(R) gravity
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Solar system constraints on f(T) gravity
• $f(T)$ models with phantom divide line crossing
• Degrees of freedom of $f(T)$ gravity
• Growth factor in f(T) gravity
• Observational information for f(T) theories and Dark Torsion
• Spherical symmetry in $f(R)$-gravity
• Conformal transformation in $f(T)$ theories
• Static Solutions with Spherical Symmetry in f(T) Theories
• Static spherically symmetric perfect fluid solutions in $f(R)$ theories of gravity
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Attractor Solutions in f(T) Cosmology
• Spherically symmetric spacetimes in f(R) gravity theories
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
• The interior spacetimes of stars in Palatini f(R) gravity
• Emergent universe in chameleon, f(R) and f(T) gravity theories
• Finite-time future singularities models in $f(T)$ gravity and the effects of viscosity
• Accelerating cosmology in F(T) gravity with scalar field

Cited by in corpus (2)

• Anisotropic Universe Models in f(T) Gravity
• Energy conditions bounds on f(T) gravity