Here's my thoughts. If 2 black holes "meet", the one that is much larger will absorb the smaller, like a frog eating an insect. Gulp, just goes down. But if 2 approximately equal size black holes meet its a different situation. To explain:
I think there’s a lot of confusion out there about black holes, mostly caused by so many people repeating the illogical argument that black holes are a point singularity. They use the incorrect argument that anything within the event horizon (Schwarzschild radius) must have energy greater than mc^2 if it is not to proceed to the center. This is getting facts backwards. The maximum gravitational energy of a star is (0.6GM^2)/R. If ALL a star’s energy goes into creating pressure, that energy would equal Mc^2 maximum. Setting Mc^2 = (0.6GM^2)/R results in the minumum radius R for anything, or any star, including the star in a black hole, of R(min) = (0.6GM)/(c^2). This is 30% of the Schwarzschild radius. Any smaller radius would mean the gravitational energy would have to exceed Mc^2.
Actual stars in nature have density profiles of about 1/(r^2), resulting in a gravitational energy of almost exactly (1.0GM^2)/R, or simply (GM^2)/R. And if all (or almost all) the mass inside a black hole were to go “relativistic” (I hate using that term), the total energy creating pressure would be (Mc^2)/3. The viral theorem, which is used to calculate the size of gravitational objects, says the energy creating pressure equals half the gravitational energy, or (Mc^2)/3 = (GM^2)/2R. This gives the radius of a star inside a black hole of R = (1.5GM)/(c^2), which is 75% of the Schwarzschild radius. It doesn’t matter what this star in a black hole is made of, quark matter, radiation, whatever; that's the size. Other basic math shows that the core density of a resulting black hole is about 20 times the core density of a neutron star, and the core pressure of the black hole is about 50 times the core pressure of a neutron star (of a few solar masses). Nothing profound or unrealistic about this. Maybe I shouldn't bother mentioning this, but also, if the star inside a black hole has an “atmosphere” of radiation, it would be small and insignificant and would not affect the above calculations. This hypothetical radiation wouldn’t come anywhere near the Schwarzschild radius and would be contained in much the same way the Earth contains its atmosphere.
An interesting result of the above is if two EQUAL mass orbitting black holes merge, there can be a huge ejection from them or even annihilation of the 2 black holes. Hmmm. Its only a matter of time before black hole mergers will be observed. Let's hope some observed mergers are of equal sized ones.
Finally, I don’t know why so many people use the Tolmann Volkov equation for a black hole. Not only does it give the wrong answer (neutron star collapse at 0.7 solar mass), but its conclusion of infinate pressure at the Schwarzschild radius is kind of obvious nonsense. But I do agree with Tolmann Volkov that the contents of a black hole can be analyzed as a gas, but one where the "gas" pressure P = (rho/3)c^2. Sorry for the length of this. If anyone has any questions on the above email Berniepie at aol.com or ask here.