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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?

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flippiefanus
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  • Hi flippiefanus. I think the question I've linked is a duplicate of yours, but if you disagree ping me and I'll reopen the question. – John Rennie Nov 06 '16 at 07:00
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    Flippiefanus, This may be a duplicate or not, but there is something wrong with your assumptions. Neutron stars have no problem being shredded and releasing matter and energy. There is no such conservation law. The final mass need not be the same as the mass of the two, it'll be smaller. They will release gravitational radiation during the in spiral, but as they get really close a lot of energetic interactions will happen that can include jets of electromagnetic radiation and gamma ray bursts. Also more gravitational radiation. See a review as of 2012 at https://arxiv.org/abs/1204.3858. – Bob Bee Nov 06 '16 at 07:16
  • @JohnRennie: If it is a duplicate it is a duplicate. I didn't see this one. Unfortunately, again no definitife answer. Anyway, I may try to change the question later to see if I can have it reopened. – flippiefanus Nov 07 '16 at 04:01
  • @BobBee. The conservation I'm referring to is baryon number, but I do understand that it would not really prevent a change in the total mass of the neutron star. However, any change in the mass should, according to my understanding, be due purely to the final state and not because of any dynamics that brought it there. The gravitational waves are due to the dynamics. Perhaps I'll try to think abotu this carefully and then rephrased my question. – flippiefanus Nov 07 '16 at 04:05
  • Two things can happen when two neutron stars collide. One is form a black hole, if the mass works out large enough. The other one is they remain as one neutron star. In the first case baryon numbers dissappear and gravitational radiation appears, and big jets of gamma radiation lasting maybe a couple seconds also. Forget baryon number. If they remain as a single neutron star they emit lots of baryons in the jet, not as powerful as the black hole jets. Those that remain include some protons, lots of neutrons and some electrons. In the core, maybe quarks and gluons. Mass is lost either way – Bob Bee Nov 07 '16 at 05:30
  • @Rennie. This question is more than about BHs, it's about two neutron stars colliding and maybe merging into a neutron star, maybe a BH. It depends on how much mass they keep. I think it's an interesting question where does the gravitational wave energy come from if they remain as a neutron star. It will be some orbital energy as they spiral in, but it will also occur from very energetic gravitational interactions as they merge, and matter (baryons, probably other charged particles) will also be emitted for them to come to equilibrium. Or they could form a BH – Bob Bee Nov 07 '16 at 05:41
  • @BobBee. Yes, I can understand that jets would remove some baryonic matter, but, do they always need to do that? Can we assume that nothing like that occurs? So, if we can ignore the loss of matter due to mechanisms like that and only consider gravitational waves, is there a mechanism that would remove mass via gravitaiotnal waves? – flippiefanus Nov 08 '16 at 04:44
  • I assume you mean if they marge to a neutron star. Good question, have to think about it. Will reply. – Bob Bee Nov 08 '16 at 18:56
  • There are mechanisms, they involve the asymmetric density and pressure and angular momentum as they merge and some pretty complex dynamics are going on. The binary neutron star merger dynamics depends to a certain extent on the nuclear equation of state, partly how soft or hard it is (how compressible), and at those neutron star densities there is no certainty on it, so calculations are done for a variety of them and parameters. So energy can be released in EM, gravitational, particles, and it can be compression inside or even changes of state (eg, neutrons to quarks). Ask a question – Bob Bee Nov 10 '16 at 06:17
  • I don't know how to phrase such a question without it being identified as a duplicate again. – flippiefanus Nov 10 '16 at 06:21

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