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Ultimately it is doesnt matter what Einstein believed. He has been shown to be wrong on other occasions such as quantum entanglement. So whether he believed in the existence of gravitational waves or not is a moot point and to use the statement that he didn't believe in gravitational waves to argue against st their existence is an appeal to authority logical fallacy.
To make a point regarding the final paragraphs of the paper. This is not really a proof that gravitational waves do not exist. Merely it is a point that when using small accelerations then the equations simply become Newtonian, which is what we would expect. And this is alright because it is the large accelerations which produce gravitational waves.