Ok I am wondering what would happen if an anti-black hole collided with a black hole of the same mass. Would they annihilate and release energy or would it become a more massive or less massive black hole?
This is a little subtle. I originally posted that it was not true that they had negative mass. Actually I think it's more complex than that. On the Penrose diagram for a maximally extended Schwarzschild metric, you have a whole separate universe in which the definition of energy is negated. It's not obvious to me how to apply that to a universe in which both a black hole and a white hole are accessible from the same external space.They would need a negative mass, and repel masses, so I doubt that they could merge with a black hole.
I don't think this is the kind of question that makes sense in GR. Answering it would require saying the location "now" of whatever stuff went into forming the black hole by gravitational collapse. GR doesn't give an unambiguous definition of simultaneity as measured by a distant observer. For example, if a charged particle is released near a black hole, a distant observer can say that the particle approached the event horizon asymptotically but never got through (because of infinite time dilation), or he can say that it reached the singularity a long time ago. Neither of these is right or wrong. Therefore we can't say where the charge resides. I'm giving an example that involves the formation of the black hole by gravitational collapse, but I don't think the answer is changed if you consider an eternal black hole; quantities like mass and charge are still not localizable according to a distant observer.And these properties reside at or outside the event horizon?