Classification of static plane symmetric spacetime via Noether gauge symmetries

Abstract

In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions [Formula: see text], [Formula: see text] and [Formula: see text]. Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between [Formula: see text], [Formula: see text] and [Formula: see text]. For all cases, different forms of unknown functions of radial factor [Formula: see text] are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1–4 is presented.