Killing and Noether Symmetries of Plane Symmetric Spacetime

TL;DR

This paper investigates the Killing and Noether symmetries of various static plane symmetric spacetimes, including Minkowski, Taub's universe, and anti-de Sitter, revealing their algebraic structures and relationships.

Contribution

It provides a comprehensive analysis of Killing and Noether symmetries for multiple plane symmetric spacetimes, including special cases and gauge terms, expanding understanding of their algebraic properties.

Findings

Lie algebra of Minkowski spacetime is 10-dimensional for Killing symmetries.

Lie algebra of Minkowski spacetime is 17-dimensional for Noether symmetries.

Noether generators include gauge terms and support the conjecture that Killing symmetries form a subalgebra of Noether symmetries.

Abstract

This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkwoski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub's universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries [1].