# Can stress energy tensor vanish in general relativity?

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?

• @CuriousOne: oops, I meant electron + positron not electron + proton - I've corrected my comment. My question still stands: what conservation laws are violated by an electron and positron annihilating to two gravitons? Sep 23 '15 at 11:24
• @CuriousOne: why does $e^- + e^+ \rightarrow 2g$ violate the equivalence principle? That's a genuine not a rhetorical question. Sep 23 '15 at 11:30
• @CuriousOne: I have to confess that your reasoning escapes me. But we'll get shouted at by a moderator if we continue here, and more importantly I want my lunch now. Sep 23 '15 at 11:33
• Sep 23 '15 at 12:39
• @Ballistics: Then you may be interested in this question and the answers there physics.stackexchange.com/questions/4015/…
– MBN
Sep 24 '15 at 7:03