Invariance analysis and conservation laws of the wave equation on Vaidya manifolds

Abstract

In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds.

On the invariance properties of Vaidya-Bonner geodesics via symmetry operators

“…where η α ,(0) = η α (s, x) and D is the total derivative operator. The invariance of the system (3) under the one-parameter Lie group of transformations (10) leads to the invariance criterions. So X is a point symmetry generator of (3) if and only if…”

“…In, [9,10], the authors present a complete analysis of symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. Now in this paper, we try to find Lie point symmetries and Noether symmetries for the Vaidya-Bonner metric…”