Abstract
By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitational wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the casuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.
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