Why can black holes accelerate if they have infinite mass?

[hazhar]

as a warning, my knowledge of physics is purely on the level of 'mild interest'. Any innacuracies/stupidities in the following post are because of this, and I hope you'll make allowances for my layman status

basically, I'm confused as to how black holes 'move'. My understanding of relativity is that the more massive an object, the more energy it requires to accelerate... but my understanding of the nature of a black hole is that it is infinitely massive... Does that mean a black hole requires infinite energy to accelerate, even a tiny amount? That seems like a mildly valid situation... but say we have 2 black holes, very close to each other. Presumably their gravity will cause them to move towards each other... but where is the energy for this move coming from? And would an encounter with another black hole be the only situation in which a black hole will move?

I hope that makes enough sense for you to be able to explain what the solution to this is

 

[Integral]

but my understanding of the nature of a black hole is that it is infinitely massive...

Here lies a basic problem, black holes do NOT have an infinite mass. There mass is finite but the density of the mass approaches infinity.

 

[hazhar]

Here lies a basic problem, black holes do NOT have an infinite mass. There mass is finite but the density of the mass approaches infinity.

heh. i thought it would be something simple like that. nevermind then...