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Is there any theory that gets rid of gravitational wave and still matches with all correct predictions made by standard physics theories? (e.g. General Relativity)

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This is not possible at long distances because of special relativity. If gravity is a long-range force, the effects must be transmitted at the speed of light, so that there must be gravitational waves. The reason is that if you shake a mass at one point, the different position of the mass must lead other masses far away to shake later, at the speed of light. The outward propagating pulse that tells the masses where the mass is is the gravitational wave.

Further, there is experimental data on binary pulsars that show the energy carried off by gravitational waves. While we don't have direct evidence that this is what is going on, the pulsar decay period is consistent with the predictions of General Relativity regarding the waves.

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+1 Gravitational Waves And Propigating Fields of force are governed by specific observable laws. – Argus Jun 5 '12 at 1:37

I heard about no such theory. If space itself is a dynamic structure, which means it could change, then wave may be a necessary part of such theory

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