Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame

Abstract

A complete perturbation theory suitable for teleparallel gravity is developed. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation scheme can be transformed to one in which perturbations all take place within the co-frame. A covariant definition of a teleparallel Minkowski geometry is proposed. We compute the perturbed field equations for $f(T)$ teleparallel gravity and discuss the stability of the teleparallel Minkowski geometry within $f(T)$ teleparallel gravity.

arXiv comment33 pages, Published in Universe

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Cited by in corpus (4)

• Spherically symmetric teleparallel geometries
• Static spherically symmetric perfect fluid solutions in teleparallel F(T) gravity
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Scalar Field Static Spherically Symmetric Solutions in Teleparallel $F(T)$ Gravity