Momentum transfer when object falls into black hole

[Ookke]

Let's imagine a stationary black hole and a fast moving object falling into BH. Let the momentum of the falling object be enough to give an observable bump to BH, pushing it into motion.

Since the object does fall into BH, by momentum preservation BH should start moving. But I don't see how this could happen, because due to relativistic time dilation, the falling object never actually reaches the event horizon of the BH (from outside observer's point of view), let alone the singularity.

So it seems that the empty space (or perhaps the gravitation field itself) is somehow able to transfer the falling object's momentum to the singularity, without even touching. Any ideas how this could be solved? Thanks.

 

[Chronos]

How does momentum transfer work on Earth when a meteor crashes into it?

 

[.Scott]

How does momentum transfer work on Earth when a meteor crashes into it?

Ookke isn't asking about work or energy, just momentum. If we take a planet with no atmosphere, a cannon ball fired at the planet will at first cause the planet to move toward the cannon ball because of gravitational attraction. Then the cannon ball will strike the planet in an inelastic collision pushing the planet back.

The same basic thing will happen when a cannon ball is fired into a black hole, but the collision is a bit more difficult to describe. One problem is the interaction between the black hole and the cannon ball will not be exactly like an inelastic collision. A large percent of the mass of the cannon ball will be release as radiation. But if we ignore that - and a couple of other inconveniences, we can imagine an more-or-less intact cannon ball approaching the event horizon.

As the cannon ball approaches the event horizon, it will appear to increase in mass and slow. But even without a collision, the gravitational field of the cannon ball and that of the black hole will blend to form a single field representing the total mass with momentum conserved. Two things that the black hole does not hide is the total mass and momentum of the objects it has feasted upon.

 

[Ookke]

Thanks .Scott for your clear answer, this is much more understandable now. I find it interesting that gravitation field can not only pull things together, but also (at least in some sense) act as a medium for momentum transfer.

It's quite strange that cannon ball doesn't collide with black hole but freezes at event horizon, but this becomes more understandable if we remember that BH isn't exactly an object. BH is sometimes visualized as stellar object like planet, star etc, but it's locally something quite different. At distance BH of course acts like any stellar object with same mass.

 

[tarzan322]

My understanding is that the information of the object is imprinted on the Event Horizon as it crosses it, and is the reason it appears to slow to the point it stops. The mass of the object itself however is added to the mass of the Black Hole as the object is shredded into it's constituent bits of matter by the gravitational effects of the Black Hole, and the object never gets a chance to reach the singularity in one piece, so momentum would no longer be a sizable issue.

 

[Ookke]

the object never gets a chance to reach the singularity in one piece, so momentum would no longer be a sizable issue.

Momentum conservation should work, even if the object is shattered or changes its form to e.g. radiation.