If an anti-matter singularity and a normal matter singularity, of equal masses, collided would we (outside the event horizon) see an explosion?
Black holes and "anti"-black holes are the same objects. A black hole resulting from the collapse of normal matter, and a black hole resulting from the collapse of antimatter, are indistinguishable. Recall that black holes only have charge, mass, and spin and there is no way to tell that a black hole originally was matter or not (e.g., we can't measure B or L of a black hole).
So what we see would be the same as any other two black holes colliding.
When matter and antimatter meets we see an explosion but no additional mass/energy is created. What happens is that matter is converted to energy while the total mass/energy is constant. So when the "matter" black hole and the "antimatter" black hole merge, the total mass/energy of the resultant black hole will be equal to the sum of the mass/energy of the two original black holes (minus whatever gravitational radiation is emitted during the merger). So there certainly will not be any explosion outside the black hole and in fact there probably won't be an explosion inside the black hole either. If there is any matter-antimatter annihilation the total mass/energy of the black hole will not change.
Further, the no-hair theorem states that the only quantum numbers a black hole can have are mass, electrical charge and angular momentum. So the matter/antimatter quantum numbers will not be visible outside the blach hole. I don't think we quite have a "proof" of the no-hair theorem, but most physicists think it is true.
We can't observe anything from behind the event horizon, and no tricks with ropes or rockets can get around this (see the river model of a black hole for more details), so what happens inside is irrelevant. The event horizons would merge into a single black hole (like normal).
I don't know why people are repeatedly saying nothing would happen, and it would just become a more massive black hole. :/
You could say that the two singularities would never touch, and thus annihilation would never happen. How could two infinitesimally small singularities ever touch? But you could have stars on the verge of collapse as Dizchord mentioned. In which case as the stars collided there would be a massive conversion of mass to energy, and a fairly impressive explosion.
Assuming all of the matter annihilated in a pair of 2 solar mass dense neutron star, that would be about 2.7119878813440003e+32 megatons of explosive force. That's much much much more than the largest supernova.
There's also a question of whether gravity attracts or repels antimatter. In this case it would be unlikely that a pair of super massive matter and antimatter bodies would ever meet.
"This is a question, the answer is definitely "no". – Ron Maimon" Annihilation would occur if the mass of each body actually met.
"Black holes and "anti"-black holes are the same objects. A black hole resulting from the collapse of normal matter, and a black hole resulting from the collapse of antimatter, are indistinguishable." They might be indistinguishable, but they certainly are not the same thing! Whenever matter and antimatter meets you get an explosive, 100% efficient, conversion of mass to energy. So a blackhole and anti-blackhole meeting may be quite destructive, if the matter actually collided. There's also the question of: does gravity attract or repel antimatter?
" So when the "matter" black hole and the "antimatter" black hole merge, the total mass/energy of the resultant black hole will be equal to the sum of the mass/energy of the two original black holes (minus whatever gravitational radiation is emitted during the merger). So there certainly will not be any explosion" True, the mass/energy total will be the same, however if annihilation occurred, there would be a net change in gravity. If enough matter and antimatter collided, the mass would convert to energy which is massless, and which does not create gravity. If all of the matter and antimatter collided you would see a 100% conversion from mass to energy, and a 100% reduction in gravity. Without gravity there's nothing holding the blackhole together.