Spherically symmetric teleparallel geometries

Abstract

We are interested in the development of spherically symmetric geometries in $F(T)$ teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric compatible, spin connection. We then analyse the antisymmetric field equations (the solutions of which split into two cases, which we subsequently consider separately), and derive and analyse the resulting symmetric field equations. In order to further study the applications of spherically symmetric teleparallel models, we study $3$ subcases in which there is an additional affine symmetry so that the resulting field equations reduce to a system of ordinary differential equations. First, we study static spherical symmetric geometries and solve the antisymmetric field equations and subsequently derive the full set of symmetric field equations. In particular, we investigate vacuum spacetimes and obtain a number of new solutions. Second, we consider an additional affine frame symmetry in order to expand the affine frame symmetry group to that of a spatially homogeneous Kantowski-Sachs geometry. Third, we study the special case of spherical symmetry with an additional fourth similarity affine vector.

53 pages, no figure, To appear in EPJC

References in corpus (38)

• f(T) teleparallel gravity and cosmology
• Modified teleparallel gravity: inflation without inflaton
• Teleparallel Gravity: From Theory to Cosmology
• On Born-Infeld Gravity in Weitzenbock spacetime
• Dynamical systems applied to cosmology: dark energy and modified gravity
• The covariant formulation of f(T) gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• On the covariance of teleparallel gravity theories
• Dynamical behavior in $f(T,T_G)$ cosmology
• Modified teleparallel theories of gravity in symmetric spacetimes
• Weak-Field Spherically Symmetric Solutions in $f(T)$ gravity
• Regularizing role of teleparallelism
• Spin Connection and Renormalization of Teleparallel Action
• Constraining f(T) gravity in the Solar System
• Static spherically symmetric black holes in weak f(T)-gravity
• Exact Spherically Symmetric Solutions in Modified Teleparallel gravity
• Symmetry and Equivalence in Teleparallel Gravity
• Approaches to spherically symmetric solutions in f(T) gravity
• Bianchi type-I, type-III and Kantowski-Sachs solutions in f(T) gravity
• Modified gravity: a unified approach to metric-affine models
• Exploring Axial Symmetry in Modified Teleparallel Gravity
• Complete classification of cosmological teleparallel geometries
• Scalarized Black Holes in Teleparallel Gravity
• General cosmological perturbations in teleparallel gravity
• Teleparallel axions and cosmology
• Kantowski-Sachs Universe Models in $f(T)$ Theory of Gravity
• A frame based approach to computing symmetries with non-trivial isotropy groups
• Riemann-Cartan Space-times of Gödel Type
• Cosmological dynamical systems in modified gravity
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Thick accretion disk configurations in the Born-Infeld teleparallel gravity
• Teleparallel Killing Vectors of Spherically Symmetric Spacetimes
• Generalized Teleparallel de Sitter geometries
• Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypes
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
• Spatially Homogeneous Teleparallel Gravity: Bianchi I
• Teleparallel Geometry with a Single Affine Symmetry
• Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame

Cited by in corpus (13)

• Static spherically symmetric perfect fluid solutions in teleparallel F(T) gravity
• Kantowski-Sachs spherically symmetric solutions in teleparallel $F(T)$ gravity
• Cosmological solutions in teleparallel $F(T,B)$ gravity
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Scalar field source Teleparallel Robertson-Walker F(T)-gravity solutions
• Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames
• On black holes in teleparallel torsion theories of gravity
• On black holes in new general relativity
• Electromagnetic Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Scalar Field Static Spherically Symmetric Solutions in Teleparallel $F(T)$ Gravity
• Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity
• Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions
• Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions