Approximate Noether Symmetries from Lagrangian for Plane Symmetric Spacetimes

TL;DR

This paper extends the concept of approximate Noether symmetries to general plane symmetric spacetimes by introducing a time conformal factor, providing a broader framework for understanding symmetries in perturbed gravitational fields.

Contribution

It generalizes previous work by considering the most general plane symmetric static spacetime with a time conformal perturbation to find approximate Noether symmetries.

Findings

Derived all Lagrangians admitting approximate Noether symmetries for perturbed plane symmetric spacetimes.

Extended the method to the most general plane symmetric static spacetime with a time conformal factor.

Provided a framework for analyzing symmetries in perturbed gravitational fields.

Abstract

Noether symmetries from geodetic Lagrangian for time-conformal plane symmetric spacetime are presented. Here, time conformal factor is used to find the approximate Noether symmetries. This is a generalization of the idea discussed by I. Hussain and A. Noether symmetries from geodetic Lagrangian for time-conformal plane symmetric spacetime are presented. Here, time conformal factor is used to find the approximate Noether symmetries. This is a generalization of the idea discussed by I. Hussain and A. Qadir [3,4], where they obtained approximate Noether symmetries from Lagrangian for a particular plane symmetric static spacetime. In the present article, the most general plane symmetric static spacetime is considered and perturb it by introducing a general time conformal factor $e^{\epsilon f(t)}$, where $\epsilon$ is very small which causes the perturbation in the spacetime. Taking the perturbation up to the first order, we find all Lagrangian for plane symmetric spactimes from which approximate Noether symmetries exist. PACS 11.30.-j-Symmetries and conservation laws PACS 04.20.-q-Classical general Relativity