Apparent horizon buildup in a BH merger I just read some articles about binary BH merger simulation. These state that at a certain instant a common apparent horizon(or MOTS)
appears, surrounding the two BHs. This instant is called the bifurcation time.
My question is why is it a complete closed surface? In a configuration without spatial symmetries why cannot appear AH in a single point and the grow to a closed surface?
 A: Each of the black holes in the initial conditions of this type of simulation typically have their own apparent horizon that is already a closed (non-singular) surface.  That's often what's meant by saying there are two black holes in the initial data.  The moment in time that you're describing when "at a certain instant a common apparent horizon .. appears" is almost certainly the time when those two disjoint apparent horizons connect to create a single (no longer disjoint on the spatial slice) apparent horizon that contains both singularities.
(It might still be that there's a singular moment in coordinate time when the surfaces touch at a point on the spatial slice, but I'm guessing, without seeing the details of the paper that you're reading, the authors ignored that detail.)
If you think this doesn't describe the situation in the paper you're reading, then please provide more detail or a reference to the paper.
If you started with different initial data - say a collapse process - I think what you described could happen, namely the apparent horizon could at some point in coordinate time be a single point on the corresponding spatial slice and then grow.
