LIGO is reputed to have detected gravitational waves from the merger of 2 black holes (BHs). For an external observer of such an event, each BH would appear to approach the event horizon of the other, but never cross it in a finite time......is this correct so far? But the event horizons are roughly spheres, so this approach would appear to force at least a small intrusion of one or both BHs into a 4th spatial dimension, the merged object appearing as a topological 3-sphere to the external observer. By analogy, in a 2-D universe, the merger of 2 disk-shaped BHs at their circular event horizons would force the merged object into a 3rd spatial dimension, forming a 2-sphere (a balloon). Am I imagining this scenario correctly, or if not, why not?