Energy Conditions and Conservation Laws in LRS Bianchi Type I Spacetimes via Noether Symmetries

Abstract

In this paper, we have completely classified the locally rotationally symmetric (LRS) Bianchi type I spacetimes via Noether symmetries (NS). The usual Lagrangian corresponding to LRS Bianchi type I metric is used to find the set of determining equations. To achieve a complete classification, these determining equations are generally integrated to find the components of NS vector field and the metric coefficients. During this procedure, several cases arise which give different Noether algebras of dimension , 11, and 17. A comparison is established between the obtained NS and the Killing and homothetic vectors. Corresponding to all NS generators, the conservation laws are stated by using Noether’s theorem. The metrics which we have obtained as a result of our classification are shown to be anisotropic or perfect fluids which satisfy certain energy conditions.

Scalar field cosmology via Noether symmetries in energy–momentum squared gravity

“…Capozziello and Laurentis [23] examined the NS technique in the framework of quantum cosmology. Ali and Hussain [24] investigated positive energy bounds via NS technique in Bianchi type-V universe model, whereas this work for Bianchi type-I spacetime has been studied in [25].…”