Black Holes & Particle Collisions: Does Linear Momentum Transfer?

[apamirRogue]

Now I know that in the general Schwarzschild metric, there is energy and angular momentum conservation, but what I'm wondering is if there is any linear momentum conservation. Let's say a particle collides with a black hole. Does the energy of that particle go solely to the rest mass and temperature of the black hole, or does it impart a slight impulse to the black hole? In simpler terms, can you move a black hole by just shooting enough particles into it?

 

[PeterDonis]

A black hole is not an ordinary object, so many intuitions about how ordinary objects behave do not apply to black holes. In this particular case, I don't know that the question has been studied. The Schwarzschild metric describes a black hole whose state of motion does not change, so to speak; you would need a different metric to describe a hole which has enough particles shot into it to impart an impulse, if that's possible. I've never seen such a metric described, so I don't know if the answer to your question is known.