Recently, we heard about the detection of gravitational waves. The source of these wave are believed to be two black holes that merged. One of the most amazing things about this discovery is the phenominal amount of energy that was released in the process. Where does this energy come from? This question was addressed here, so I won't repeat that question. (However, I find those answers somewhat contradictory and therefore unsatisfactory.) Instead, what I want to know concerns a slightly different scenario.
Let's consider a system of neutron stars orbiting their common center of mass as a binary system. The system would be losing energy due to gravitation waves. Eventually the two neutron stars would merge to become one, by which time the gravitational radiation would stop.
Now where did the total amount of energy that was radiated as gravitational waves come from? In my view, this could not have come from the mass of the neutron stars, because conservation laws would dictate that the combined neutron star must consist of exactly the same amount of matter that the original two stars consisted of. The other sources of energy in the system would be the kinetic energy due to the orbiting velocities and then of course a large amount of potential energy due to the separation between the two neutron stars.
So, am I right is saying that in this case the energy has to be provided purely by kinetic and potential energy in the system and not from the masses of the two bodies?
And if this is so, why wouldn't it also be the case when the two bodies happen to be black holes?
