Exact Spherically Symmetric Solutions in Modified Teleparallel gravity

Abstract

Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper we use the Noether's symmetry approach for a modified Teleparallel theory of gravity labelled as $f(T,B)$ gravity where $T$ is the scalar torsion and $B$ the boundary term. Using the Noether's theorem, we were able to find exact spherically symmetric solutions for different forms of the function $f(T,B)$ coming from the Noether's symmetries.

22 pages; Matches published version in Symmetry

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• Teleparallel Gravity: From Theory to Cosmology
• Spherically symmetric configuration in $f(Q)$ gravity
• Weak Field Limit and Gravitational Waves in $f(T,B)$ Teleparallel Gravity
• A class of static spherically symmetric solutions in $f(Q)$-gravity
• Black Holes in $f(T,B)$ Gravity: Exact and Perturbed Solutions
• Solar System Tests in Modified Teleparallel Gravity
• Gravitoelectromagnetism, Solar System Test and Weak-Field Solutions in $f(T,B)$ Gravity with Observational Constraints
• Static spherically symmetric black holes in weak f(T)-gravity
• Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics
• Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions
• Approaches to spherically symmetric solutions in f(T) gravity
• Exploring Axial Symmetry in Modified Teleparallel Gravity
• Testing Born-Infeld $f(T)$ teleparallel gravity through Sgr A${}^{\star }$ observations
• Exact spherically symmetric solutions in modified Gauss-Bonnet gravity from Noether symmetry approach
• Spherically symmetric teleparallel geometries
• Inflation with F(T) Teleparallel Gravity
• General Teleparallel Modifications of Schwarzschild Geometry
• Static spherically symmetric perfect fluid solutions in teleparallel F(T) gravity
• A viable form of the metric Teleparallel F(T) theory of gravity
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• Focusing conditions for extended teleparallel gravity theories
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• Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions
• Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions