Propagation of gravitational waves in Robertson-Walker backgrounds
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The electric and magnetic parts of the linearized Weyl tensor, when the stress-energy tensor is that of a perfect fluid and the background is of Robertson-Walker type, are known to satisfy wave equations that differ by the presence of a source term for the electric part. It is shown here that all of the allowed solutions of the inhomogeneous equation can be obtained by applying a differential operator to the solutions of the homogeneous equation; consequently, electric-type and magnetic-type gravitational waves have the same propagation properties. The results of a complete integration of the appropriately linearized Newman-Penrose equations are given.
KeywordsWave Equation Differential Operator Source Term Propagation Property Differential Geometry
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