Partial-Differential Equations, Conservation-Laws, Noether, Separation, Variables
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.
Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Kara, A. H.; and Karim, Munawar (2011). "Wave Equation on Spherically Symmetric Lorentzian Metrics." Journal of Mathematical Physics 52.6.
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