Noether symmetries and conservation laws of wave equation on static spherically symmetric spacetimes with higher symmetries

Abstract

In Bokhari et al. (2011), the Noether symmetries of the wave equation on a general spherically symmetric spacetime metric were provided in terms of five functions of the variables t and r subject to certain differential equations and constraints. In this work, these differential equations and constraints are solved for all the static spherically symmetric spacetimes admitting G10 or G7 or G6 as maximal isometry group. As a result, the Noether symmetries and the corresponding conservation laws for all static spherically symmetric spacetimes admitting higher symmetries are obtained explicitly.