LEFT: GIF frames were taken at 0.11467 millisecond intervals. The problem was commenced with each BH placed at 30 miles from the barycenter (along X-axis) and given equal but opposite Y-components of velocity of 40,982 miles/second (0.22c). The individual BH event horizons there do not overlap but soon do merge as rotation continues toward closest approach.
RIGHT: More widely separated Elliptic-Orbit 5+5Sm binaries with trajectories painted RED when Schwarzschild-or-greater energy is detected. When trajectory tracks are sub-Schwarzschild they are painted WHITE. Black denotes the individual Schwarzschild radius as though 'each opposite BH' were not there. Notice the RED growth outside the black event horizon during mutual approach; Trajectories painted RED bound the total event horizon(s) at all positions at all times. At great separation the RED horizon converges to the individual black hole EH (BLACK, Rs=2GM/c^2).
It is worth mentioning that the 2D 3-Body solver code [now] develops the exact combined Schwarzschild event horizon based on infinite-drop fully parabolic in-fall trajectories (ellipticity=1.0).
The analysis works equally well with un-equal mass black holes. I have concentrated on equal mass black holes because they are special in their ability to provide a flight path unperturbed in X and Y all along Z. Equal mass binaries with eccentricity=0 and e>0 provide balanced X-Y force cancellation. Binaries with e>0 provide another mechanism for pulsed output along the spin axis jets because the Z-acceleration is highly modulated for even moderately eccentric orbits.
The above enhanced animation is for two 10SM black holes with elliptical orbits. The view is looking into the Z-spin axis. The images are taken at equal 0.122mS increments which timing betrays the increase in orbital speed in the animation as the singularities approach. At the end of each time increment (binary motion time suspended) an array of in-fall particles are released (one at a time) from infinity in the X-Y plane for angles from 5 degrees to 175 degrees in 5 degree increments. The RED border for each 'snap-shot' denotes the combined event horizon as the binary spins. It can be seen that the combined EH approaches that of a single 20SM black hole as the two 10SM holes move past closest approach. BH Event horizon radius (Rs) is directly proportional to the mass.
If the peak separation is increased just a tiny bit, the binary would momentarily become (once per revolution) two black holes with separate (but close) event horizons. I have found that for EQ-mass BH pairs that the critical (CG) separation is equal to 4X the individual (Rs) for one BH. Will have to think of a cute acronym for black holes with this separation; maybe CARP, Critical Approach Radius Positioning.
The red boundary is just one principal element of the EH. The entire volume of the binary BH event horizon can be easily envisioned by forming a solid of revolution by rotating the red shape (at any instant in time) about an axis that passes through CG's of both black holes. The relative scale and relative timing of the animation are both accurate. Essentially, you are just looking down the "Binary BH gun barrel" where jets may emanate. Is this cool or what?
I may next make a side view of the combined EH for an Un-Equal mass binary with eccentricity (e)>0. This should show very well the scattering of in-fall orbits by an Un-Equal mass binary.