Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order

Abstract

f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation field. In this present work, we investigate specifically the range of validity of Birkhoff's theorem with the general tetrad field via perturbative approach. At zero order, Birkhoff's theorem is valid and the solution is the well known Schwarzschild-(A)dS metric. Then considering the special case of the diagonal tetrad field, we present a new spherically symmetric solution in the frame of f(T) gravity up to the perturbative order. The results with the diagonal tetrad field satisfy the physical equivalence between the Jordan and the so-called Einstein frames, which are realized via conformal transformation, at least up to the first perturbative order.

8 pages, no figure. Final version, accepted for publication in EPJC

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• Matter Density Perturbations in Modified Teleparallel Theories
• Charged Black Holes in Generalized Teleparallel Gravity
• Higgs inflation and teleparallel gravity
• The distinctions between $\Lambda$CDM and $f(T)$ gravity according Noether symmetry
• Planar Symmetry in f(T) gravity
• Generalized Birkhoff theorem in the Poincaré gauge gravity theory
• Onset of acceleration in a Universe initially filled by dark and baryonic matters in nonminimally coupled teleparallel model
• Birkhoff's theorem for stable torsion theories
• Inflation with F(T) Teleparallel Gravity
• Cosmology in a reduced Born-Infeld--$f(T)$ theory of gravity
• Solving Tolman-Oppenheimer-Volkoff equations in $f(T)$ gravity: a novel approach
• A viable form of the metric Teleparallel F(T) theory of gravity
• Generalized Noether Theorem for Gauss-Bonnet Cosmology