Colliding Black Holes

[Worzel]

I am sure this must have been asked before but here goes.

If two black holes were on a collision course with each other or would pass close to each other. Would the smaller one get pulled into the bigger one?

[stereobot]

In short, yes.

The smaller black hole would also be pulling on the larger black hole just like the moon pulls on the Earth. The issue would be the same if you were talking about the Earth and the Moon, although the actual collision would happen quite a bit differently. This is all taking into account they are on a direct collision course with each other.

[94JZA80]

well provided that a collision is imminent, i'm not so sure that one BH would consume the other BH so much as they would just merge and become a single, more massive BH, where the mass of the new BH would be the sum of the masses of the two BH's prior to the merger. but i must throw in a disclaimer - this suggestion is based only on my very limited knowledge about black hole mergers. i do not know enough on the subject to confidently say that one BH or singularity can or cannot "consume" another of its kind.

[Nabeshin]

Yes, the two black holes will coalesce as described into a single black hole with surface area greater than the sum of the surface areas of the two individual black holes. Generally, the entire process can be broken down into three distinct regimes:

1) Plunge. The black holes are relatively far away from each other and are approximately kerr-schild (i.e there is not much tidal deformation due to the curvature of the other hole). Much of this stage can actually be computed with post-newtonian approximations to general relativity, provided the holes are not too close together.
2) Merger. The black holes get close and are extremely distorted as they come together and the event horizons of each black hole reach out and touch with each other (when you can say they have truly merged). Things are very complicated during this stage, and numerical modeling is the only way to get any results.
3) Ringdown. Once a single event horizon has emerged, it will oscillate from its strange distorted shape down to a kerr-schild horizon that one would expect. This part is rather like the ringing of a bell which slowly damps away its oscillations to become a static solution. This part is (relatively) easy, as these oscillations modes can actually be computed analytically with approximations to general relativity.

I can answer (hopefully!) any questions you have about any of the three regimes or anything in general about merging black holes, as it is a line of research I am currently involved in.

[Chronos]

Depends on mass and velocity at closest approach. Nabeshin gave the detailed answer. In any event, neither will 'decompose' under any circumstances. They will either merge or go on their merry way.