Noether symmetries of vacuum classes of pp-waves and the wave equation

Abstract

The Noether symmetry algebras admitted by wave equations on plane-fronted gravitational waves with parallel rays are determined. We apply the classification of different metric functions to determine generators for the wave equation, and also adopt Noether's theorem to derive conserved forms. For the possible cases considered, there exist symmetry groups with dimensions two, three, five, six and eight. These symmetry groups contain the homothetic symmetries of the spacetime.

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Classification of the Lie and Noether Symmetries for the Klein–Gordon Equation in Anisotropic Cosmology

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