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Imagine 2 non-spinning black holes with identical mass collides with each other at the same speed in the absence of other matter, I think the gravitational waves can only carry a little of the momentum but how about the rest which cannot be imparted to falling matter since it is initially vacuum? Normally when 2 objects collides, the momentum is distributed according to Newton 3rd law and heat as well but on the case of black hole no heat is produced and gravitational wave cannot carry the balance momentum also black hole don't knock back each other.

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  • $\begingroup$ If you transform to the reference frame where both objects have opposite and equal momentum then the final object plus waves will also have zero total momentum. $\endgroup$ – my2cts Dec 18 '19 at 9:23
  • $\begingroup$ Black holes certainly count as matter. You may mean that no accretion disks are present. $\endgroup$ – my2cts Dec 18 '19 at 9:26
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    $\begingroup$ A black hole of mass $m$ moving at a velocity $v$ carries a momentum $mv$ just like ordinary matter does, so it isn't clear what the problem is. Can you clarify why you think there might be a problem with conservation of momentum? $\endgroup$ – John Rennie Dec 18 '19 at 11:29
  • $\begingroup$ @JohnRennie: I've edited the question to better state the problem I'm facing. $\endgroup$ – user6760 Dec 18 '19 at 11:59
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    $\begingroup$ the momentum is distributed according to Newton 3rd law and heat This doesn't make sense. Heat is a form of energy, not momentum. In general, I'm not able to make any sense out of this question. $\endgroup$ – user4552 Dec 18 '19 at 15:00
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If two black holes with the same mass collide head on at the same speed, the total momentum is zero. What you may be asking is not momentum, but the kinetic energy of the black holes moving toward each other. After the collision, the mass of the resulting larger black hole will consist of the masses of two original black holes plus their kinetic energy minus the energy emitted in gravitational waves ($c=1$).

In a simpler example, if a small relativistic particle with a relatively large kinetic energy hits a black hole, the mass of the black hole is increased by the total energy of the particle or the sum of its mass and kinetic energy (neglecting gravitational waves).

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