Symmetry analysis of wave equation on static spherically symmetric spacetimes with higher symmetries (original) (raw)

Wave equation on spherically symmetric Lorentzian metrics

Journal of Mathematical Physics, 2011

Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of θ and φ are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.

Symmetry analysis of wave equation on sphere

Journal of Mathematical Analysis and Applications, 2007

The symmetry classification problem for wave equation on sphere is considered. Symmetry algebra is found and a classification of its subalgebras, up to conjugacy, is obtained. Similarity reductions are performed for each class, and some examples of exact invariant solutions are given.

Complete classification of spherically symmetric static spacetimes via Noether symmetries

In this paper we give a complete classification of spherically symmetric static space-times by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.

On the paper “Symmetry analysis of wave equation on sphere” by H. Azad and M.T. Mustafa

Journal of Mathematical Analysis and Applications, 2010

Using the scalar curvature of the product manifold S 2 × R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave equation obtained by H. Azad and M. T. Mustafa [H. Azad and M. T. Mustafa, Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl., 333 (2007) 1180-1188] to nonlinear Klein-Gordon equations on the two-dimensional sphere. 2000 AMS Mathematics Classification numbers: 76M60, 58J70, 35A30, 70G65

Static plane symmetric spacetimes

1991

A complete classification of static plane symmetric spacetimes is provided. The previously known spacetimes are recovered (but not generally discussed) and some new spacetimes with higher symmetry found.

A new symmetry of the relativistic wave equation A new symmetry of the relativistic wave equation

In this paper we show that there exists a new symmetry in the relativistic wave equation for a scalar field in arbitrary dimensions. This symmetry is related to redefinitions of the metric tensor which implement a map between non-equivalent manifolds. It is possible to interpret these transformations as a generalization of the conformal transformations. In addition, one can show that this set of manifolds together with the transformation connecting its metrics forms a group. As long as the scalar field dynamics is invariant under these transformations, there immediately appears an ambiguity concerning the definition of the underlying background geometry.