Noether Symmetries and Conservation Laws in Non-Static Plane Symmetric Spacetime

Abstract

In this paper, we find all nonstatic plane symmetric spacetime metrics whose corresponding Lagrangians possess Noether symmetries. The set of determining equations is analyzed through a Maple algorithm that restricts the metric coefficients to satisfy certain conditions. These restrictions on metric coefficients, while using them to solve the determining equations, give rise to a number of plane symmetric metrics admitting 4-, 5-, 6-, 7-, 8-, 9-, 11-, and 17-dimensional Noether algebras. The Noether theorem is used to find a conserved quantity corresponding to each Noether symmetry. Some physical implications are discussed by finding bounds for different energy conditions for the obtained metrics.