Do colliding black holes violate time reversal symmetry? Two black holes can collide and merge into one bigger black hole, but not split into two. Does this mean colliding black holes violate time reversal symmetry?
Related: Do black holes violate T-symmetry? Based on the answer to that question, time-reversing a black hole yields a white hole. However, that seems to imply that white holes are very unstable because they can spontaneously split into two, which would then split into four, ad infinitum, and the universe would be covered with tiny white holes all over.
 A: Yes, to the same extent as falling egg violates time reversal symmetry (have you seen a broken egg spontaneously jump from the floor to your cup?). 
This is called "second law of thermodynamics" and it is not time-symmetric. 
A: You missed something: the gravitational waves.
A black hole merger spacetime contains gravitational waves leaving the merger at the speed of light. Time reversal reverses time across the entire spacetime, and this converts those escaping gravitational waves into a converging gravitational wave front, as well as the black holes into white holes. These waves converge in on the central (now-)white hole and get so strong at that central point of convergence as to be able to "buck" it apart into two separate white holes.
Without those incoming gravitational waves, such a split would not occur.
EDIT: As A.V.S. points out in the comments, in fact, a better answer to this question would be that the future evolution of white holes is in general undetermined, or better unrestricted, in the sense that multiple future trajectories from identical phase-space points will satisfy the dynamical equations, though of course that means still that we must highlight that a crucial element of the answer here is that the time reversal turns the black hole into a white hole. (Indeed, this is part of why they're called "white" - technically that's understating it: they can literally spit out anything - even unicorns, no seriously, it'd be entirely [though unlikely] consistent with the equations for a 1-horned ungulate to pop out, as much as literally anything else.)
In a realistic black hole collision case, which is what I assumed in the answer above, then of course, yes, you will have the gravitational waves and so forth and you do have to take them into account in the reversal. But the situation is even more serious.
Since the future evolution of white hole is unrestricted, you can build scenarios with a totally causeless, spontaneous split of the white hole, and have it be consistent with the dynamical equations. As it is a consistent evolution, it doesn't violate time reversal symmetry. The reason that the Universe isn't covered with tiny white holes is that they are next to impossible to form in the first place - and likely, general relativity is not the final description of these things.
(I want to point out that there is actually an analogy for this within ordinary Newtonian mechanics called "Norton's dome". It is not physically achievable, but is still a system within the mathematical theory which has a similar property of its present state being equiconsistent with multiple future evolution trajectories.)
A: When two black holes collide and merge into one, a lot of energy is sent out as gravitational waves.  This energy spreading out without bound represents an increase in entropy, along with any increase due to the final BH surface area being greater than the sum of the original two.
If we had an exact solution to Einstein's field equation describing this, we could replace t with -t and have another valid solution.  What this means in real life is that a black hole just sitting somewhere, when bombarded with converging gravitational waves arranged exactly the right way, could absorb those waves and split into black holes.  
I don't know about ultra-advanced alien technology, but anything I can imagine like that isn't going to happen. It's just like the fragments and droplets of a dropped egg coming back together just right to make an unblemished whole egg.
