Extended Birkhoff's Theorem in the f(T) Gravity

Abstract

The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011), arXiv:1107.0629v1], we prove that the Birkhoff's theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss respectively the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of the Birkhoff's theorem in the frame of f(T) gravity via conformal transformation by regarding the Brans-Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.

7 pages, 1 figure, submitted to EPJ-C. arXiv admin note: substantial text overlap with arXiv:1107.0629

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Cited by in corpus (39)

• f(T) teleparallel gravity and cosmology
• The covariant formulation of f(T) gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Good and bad tetrads in f(T) gravity
• Viable f(T) models are practically indistinguishable from LCDM
• New Schwarzschild-like solutions in f(T) gravity through Noether symmetries
• Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
• Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
• Energy conditions bounds on f(T) gravity
• New observational constraints on f(T) gravity from cosmic chronometers
• Weak-Field Spherically Symmetric Solutions in $f(T)$ gravity
• Solar System tests in $f(T)$ gravity
• A Built-in Inflation in the $f(T)$-Cosmology
• Constraining f(T) gravity in the Solar System
• Phase Portraits of general f(T) Cosmology
• Charged rotating black holes coupled with nonlinear electrodynamics Maxwell field in the mimetic gravity
• Model-independent limits and constraints on extended theories of gravity from cosmic reconstruction techniques
• FRW in quadratic form of $f(T)$ gravitational theories
• Junction conditions in extended Teleparallel gravities
• $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity
• Static and spherically symmetric wormholes in metric-affine theories of gravity
• Static spherically symmetric black holes in weak f(T)-gravity
• Geodesic Deviation Equation in $f(T)$ gravity
• Charged Black Holes in Generalized Teleparallel Gravity
• Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
• Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity
• The distinctions between $\Lambda$CDM and $f(T)$ gravity according Noether symmetry
• The tetralogy of Birkhoff theorems
• Generalized Birkhoff theorem in the Poincaré gauge gravity theory
• Violation of causality in $f(T)$ gravity
• Big Bang Nucleosynthesis constraints on $f(T,T_G)$ gravity
• Inflation with F(T) Teleparallel Gravity
• Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order
• Charged Anti-de Sitter BTZ black holes in Maxwell-$f(T)$ 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
• f(T) Quantum Cosmology
• Quantum cosmology in teleparallel gravity with a boundary term
• Generalized Noether Theorem for Gauss-Bonnet Cosmology