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A black hole binary consists of two black holes orbiting their barycenter. Gravitational waves make the pair lose the kinetic energy. The black holes eventually spiral into each other and merge into a larger black hole.

I don't have the level of understanding the exact process behind that. I know that celestial bodies may lose kinetic energy for reasons like tidal forces, collisions and gravitational perturbation of other bodies. Tidal forces may cause friction at the planet's crust and convert kinetic energy into heat. That is why, for instance the moon is tidally locked to Earth because tidal forces made it lose rotation energy that turned into heat.

The question is: Gravitational waves make the two black holes lose kinetic energy, but this energy is converted into what? If there is no other celestial body nearby that will disturb them, then where this energy goes to? Is it transferred to the space-time fabric?

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    $\begingroup$ It's converted into gravitational waves. Similar to two opposite charges spirally around each other and losing energy into electro-magnetic waves. $\endgroup$ – George Herold Dec 21 '17 at 19:14
  • $\begingroup$ @anna v's answer is right, as is George Herold's comment. While this isn't an answer, it's an analogy that — while not as precise as the electromagnetic one — is more familiar, so it might be more helpful. The analogy is that of a paddle stuck vertically into water. If you spin it around, you'll see waves spiraling outward. Those waves carry off energy, which they've robbed from the paddle — which is why you need to keep supplying energy if you want it to keep spinning. In the same way, and inspiralling binary gives up energy to the ripples in spacetime we call gravitational waves. $\endgroup$ – Mike Mar 7 '18 at 14:50
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The question is: Gravitational waves make the two black holes lose kinetic energy, but this energy is converted into what? If there is no other celestial body nearby that will disturb them, then where this energy goes to? Is it transferred to the space-time fabric?

Classical gravitational waves are a distortion on the space time, and if they cross matter they lose part of their energy in vibrations/kinetic-energy as we have seen in the LIGO detectors, which detected the waves by the tiny motions of the detectors.

If no matter, cosmic dust to stars and galaxies is met on their way they will go off to infinity.

Alternatively, effective quantization of gravity tells us that the classical gravitational waves are built up by gravitons, the analogue of photons in electromagnetism. Similar to photons, some will lose energy by interacting gravitationally with matter, and if they meet nothing on the way they will move off to infinity.

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