Approximate Noether symmetries from geodetic Lagrangian for plane symmetric spacetimes
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,5–6 where they obtained approximate Noether symmetries from Lagrangian for a particular plane symmetric static spacetime. In the present paper, the most general plane symmetric static spacetime is considered and perturbed it by introducing a general time-conformal factor eϵf(t), where ϵ 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 spacetimes for which approximate Noether symmetries exist.