When I saw the questions why matter-anti matter annihilation produces photons not gravitons, it suddenly occured to me that if the latter really happens, it means the stress energy tensor vanishes completely because gravitational wave has zero stress energy tensor. So is it allowed when the ordinary matter(particle matter or radiation matter) convert to gravitational wave in general relativity just as particle matter convert to radiation matter in special relativity? Does such process violate the Einstein's equation?
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