Abstract
One contribution of Einstein’s equation is the existence of gravitational waves. The weak gravitational waves are solutions of the linearized Einstein’s equation around a Minkowski spacetime. By using a certain coordinate freedom, waves propagate at the speed of light and propagating plane waves in z-direction gives two polarization states. The geodesic equation gives an oscillating proper distance of two rest particles when gravitational wave passes, while for proper time, no time dilatation meaning each particle has the same proper time. The fluctuation effect of gravitational waves causes ripples in spacetime making each particle feels a tidal acceleration.
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