Static Solutions with Spherical Symmetry in f(T) Theories

Abstract

The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and then we introduce a particular frame based on the conformally Cartesian coordinates. In this particular frame, the existence conditions of various solutions are presented. Our results imply that only a limited class of f(T) models can be solved in this frame. For more general models, the search for spherically symmetric static solutions is still an open and challenging problem, hopefully solvable in other frames.

18 pages, 1 figure, revised version with distinct treaments for coordinates and frames

References in corpus (27)

• f(R) theories
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Relativistic gravitation theory for the MOND paradigm
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• f(T) Gravity and local Lorentz invariance
• On Born-Infeld Gravity in Weitzenbock spacetime
• Equation of state for dark energy in $f(T)$ gravity
• Cosmological perturbations in f(T) gravity
• Observational constraints on $f(T)$ theory
• f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Black Holes in f(R) theories
• $f(T)$ models with phantom divide line crossing
• The dynamical behavior of $f(T)$ theory
• Growth factor in f(T) gravity
• Observational information for f(T) theories and Dark Torsion
• Conformal transformation in $f(T)$ theories
• Static Spherically Symmetric Solutions in F(R) Gravity
• Pure kinetic k-essence as the cosmic speed-up
• Black hole entropy in modified gravity models
• Supernova light-curve fitters and Dark Energy
• Black holes in modified gravity theories
• 1/R Correction to Gravity in the Early Universe

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