Geodesic Deviation Equation in $f(T)$ gravity

Abstract

In this work, we show that it is possible to study the notion of geodesic deviation equation in $f(T)$ gravity, in spite of the fact that in teleparallel gravity there is no notion of geodesics, and the torsion is responsible for the appearance of gravitational interaction. In this regard, we obtain the GR equivalent equations for $f(T)$ gravity which are in the modified gravity form such as $f(R)$ gravity. Then, we obtain the GDE within the context of this modified gravity. In this way, the obtained geodesic deviation equation will correspond to the $f(T)$ gravity. Eventually, we extend the calculations to obtain the modification of Matting relation.

13 pages, 7 figures

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• f(T) teleparallel gravity and cosmology
• The covariant formulation of f(T) gravity
• New observational constraints on f(T) gravity from cosmic chronometers
• Model-independent reconstruction of $f(T)$ gravity from Gaussian Processes
• Gravitational Waves in Modified Teleparallel Theories
• Bounce inflation in $f(T)$ Cosmology: A unified inflaton-quintessence field
• Bayesian analysis of $f(T)$ gravity using $f{\sigma }_8$ data
• $f(T)$ gravitational baryogenesis
• Rotating AdS black holes in Maxwell-$f(T)$ gravity
• Phase Portraits of general f(T) Cosmology
• Updated constraints on $f(T)$ models using direct and indirect measurements of the Hubble parameter
• Geodesic Deviation Equation In $f(Q)$-Gravity
• Scalar perturbations in $f(T)$ gravity using the $1+3$ covariant approach
• Generalized Energy-Momentum-Squared Gravity in the Palatini Formalism
• Cosmic Acceleration From Matter-Curvature Coupling
• Modified teleparallel gravity with higher-derivative torsion terms
• Generalized Mattig's relation in Brans-Dicke-Rastall gravity
• Geodesic Deviation Equation in $f(R,T)$ Gravity
• Onset of acceleration in a Universe initially filled by dark and baryonic matters in nonminimally coupled teleparallel model
• Models of Collapsing and Expanding Anisotropic Gravitating Source in $f(R,T)$ Theory of Gravity
• The Chaplygin gas as a model for modified teleparallel gravity?
• Reheating in a modified teleparallel model of inflation
• $f(T)$ cosmology: From Pseudo-Bang to Pseudo-Rip
• Geodesic deviation in Saez--Ballester theory
• f(T) Quantum Cosmology
• Geodesic deviation equation in Brans-Dicke theory in arbitrary dimensions
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• Covariant density and velocity perturbations of the quasi-Newtonian cosmological model in $f(T)$ gravity
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• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation