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It is said that at the binary black hole collision LIGO detected recently, the energy equivalent of 3 solar masses has been released.

Since no matter can escape a black hole, the only source I can imagine is kinetic energy, so the rest mass of the new formed black hole should then be at least the combined rest mass of the two former black holes plus maybe some extra relativistic mass from the motion they had before they merged, which might not be completely converted to gravitational waves.

If the velocity of the former black holes was like suspected c/2, their relativistic masses would be 15% higher then their rest masses. The rest mass of the black holes are assumed to be 30 solar masses each. That would rawly fit the numbers.

Also the earth and the moon do not seem to lose any mass, but they also produce tiny gravitational waves.

Is my assumption that no rest mass, only relativistic mass, so velocity is converted to gravitational waves correct, or am I overlooking something? If so, what is the mechanism to convert material from inside the former event horizons to energy radiating away as waves?

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  • $\begingroup$ I wrote something of this kind in an answer before removing it. When I tried to find the datas on the ligo site, I found a very more complicated description involving the very dynamic spins energies and specific relativistic effects. Before the contact, there are parts of the 2 BHs which are in the Sch. radius of the center of gravity $\endgroup$
    – user46925
    Commented Feb 19, 2016 at 3:53
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    $\begingroup$ and a complete answer $\endgroup$
    – user46925
    Commented Feb 19, 2016 at 4:19
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    $\begingroup$ It's not completely meaningful to split up the energies of objects in full general relativity into simple categories like "kinetic energy", "potential energy" and "rest mass", as these categorizations are very coordinate-frame dependent. We can only split the GW luminsity from the black hole because we have an exact black hole solution, and a notion of the late-time state of the black hole. $\endgroup$
    – Zo the Relativist
    Commented Feb 21, 2016 at 16:56

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I will copy from Motl's blog entry on this:

But don't overlook some numerological properties of the numbers:

36+29≠62,

36+29=62+3

What does it mean? It means that the mass of the final black hole is smaller than the sum of the initial masses by approximately 3 solar masses. What has happened with this mass? It was converted to energy, via the E=mc2 T-shirt conversion formula. And into what form of energy were the three solar masses converted? They were emitted in those gravitational waves. There's simply nothing else around the final black hole! And it took place in a few minutes – the last moments of the separate life of the two black holes. (I mention a few minutes to cover 99.99... percent of the gravitational wave energy but most of the energy is emitted within the last second or so.)

Bold mine.

So the gravitational waves were ultimately powered by a mass to energy conversion.

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  • $\begingroup$ In this article the author does not distinguish between rest mass and relativistic mass, so I'm not so sure about that. He also mentions that the earth produces waves on its way around the sun, but I can only see that the earth is losing kinetic energy, not material! $\endgroup$
    – Yukterez
    Commented Feb 21, 2016 at 19:47
  • $\begingroup$ If there is really material escaping from inside the former horizons I therefore think it must have happened in the very last moment when the 2 spheres jumped into one, but then I still don't understand the mechanism to convert this mass into some other form of energy than electromagnetic radiation. $\endgroup$
    – Yukterez
    Commented Feb 21, 2016 at 19:53
  • $\begingroup$ The earth is using kinetic energy because it is the energy at the level of general relativity equations for the gravity fields in its region. Similar that an electron rotating in a magnetic field loses kinetic energy, as it's mass does not change. For the very low gravitational fields that the earth swims through the gravitational binding + electromagnetic bindings of the matter of earth makes its mass as invulnerable. In the case of strong fields as in black holes, $\endgroup$
    – anna v
    Commented Feb 22, 2016 at 4:11
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    $\begingroup$ continued: material does not have to escape for energy to transform to gravitational waves directly. The equations allow it. That is the beauty of the GR theory and that is why this observation is a validation of the theory. The M in the excerpt is the invariant mass the holes, i.e. their energy at their rest system. He is looking at rest systemes before and after. $\endgroup$
    – anna v
    Commented Feb 22, 2016 at 4:14
  • $\begingroup$ It is similar to the energy balances we do in nuclear interactions: rest mass of nuclei before, rest mass after, the rest is energy in various forms. In GR environment it is gravitational energy. $\endgroup$
    – anna v
    Commented Feb 22, 2016 at 4:21
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First let us note that GW are ripples in space, and are created due to motion of black holes.

Therefore it should be easy to see that the waves come only from kinetic energy, which in turns comes from converting potential energy of the system into motion of the system.

Change in mass may be taking place due to other reasons/mechanisms that are not relevant to this question. Because, for "change in mass" to contribute to GW, it first have to convert to kinetic energy (of the two BH), and it is difficult to explain, how that would happen. And even if it does by some magic, would it have any noticeable contribution towards GW.

GW are ripples in space and they can only be created by kinetic energy - i.e. by movements or probably by explosions too.

If conversion of mass into energy was creating GW, then all the stars would generate GW (however weak) all the time.

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Energy is conserved. Just need to account for all forms. And in fact the 3 solar masses lost is how they figure the luminosity, and by observing the grav wave amplitude the luminosity distance.

Grav waves came from quadruple and higher moment changes, i.e., kinetic energy of the binary. Part of it was radiated. The energy of the grav wave was roughly the 3 solar masses lost.

Energy was extracted from the binary system. Still, no particles left the black holes, before or after the merger, from inside the horizons. I do not know the mechanism.

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A good chunk is rest mass. The recently observed LIGO merger resulted in a hole with two less solar masses than the sum of the masses of its predecessors. The remainder got emitted as gravitational waves.

Orbital energy, however, is the most important contributer. The kinetic energy of the binary actually increases over the in spiral; the holes go faster as they fall.

Note, however, that energy is not strictly conserved in this process, since the binary spacetime has an explicit time dependence. The above discussion is thus only heuristic.

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