Noether gauge symmetry for the Bianchi type I model in f(T) gravity

TL;DR

This paper investigates Noether symmetries in Bianchi type I models within f(T) gravity, revealing maximum symmetries and deriving specific invariants, which enhances understanding of the model's geometric and physical properties.

Contribution

It identifies the form of f(T) compatible with Noether symmetries in Bianchi type I models and classifies the symmetries, including time and scale invariance.

Findings

Maximum number of Noether symmetries in teleparallel gravity

Derivation of symmetry generators and invariants

Classification of five types of symmetries

Abstract

In this paper, we present the Noether symmetries of a class of the Bianchi type I anisotropic model in the context of f(T) gravity. By solving the system of equations obtained from the Noether symmetry condition, we obtain the form of f(T) as a teleparallel form. This analysis shows that teleparallel gravity has the maximum number of Noether symmetries. We derive the symmetry generators and show that there are five kinds of symmetries, including time and scale invariance under metric coefficients. We classify the symmetries and we obtain the corresponding invariants.