Approximate Symmetries of Lagrangians for Plane Symmetric Gravitational Wave-Like Spacetimes

TL;DR

This paper investigates the approximate symmetries of a Lagrangian describing plane symmetric gravitational wave-like spacetimes using Lie symmetry methods, revealing a non-trivial first-order approximate symmetry.

Contribution

It introduces a novel application of Lie symmetry analysis to perturbed Lagrangians of gravitational spacetimes, identifying their approximate symmetries.

Findings

Identified a non-trivial first-order approximate symmetry.

Applied symmetry methods to perturbed gravitational Lagrangians.

Enhanced understanding of symmetries in gravitational wave spacetimes.

Abstract

Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial first-order approximate symmetry.