If time stops at the event horizon, can we ever detect two black holes merging? In other words, if you are a short distance away, would you encounter a spherically symmetric gravitational field, or a dipole field?
The thing to remember whenever dealing with spacetime weirdness surrounding extremely dense objects is that what happens, that is, what the objects in question actually experience, can be completely different from what appears to happen to a distant observer.
From the point of view of the singularities at the core of each black hole, they "swirl down the drain," no problem. That is, each one spirals in faster and faster, until they merge. Things do get a little weird once the smaller singularity is inside the event horizon of the larger one, but any small object falling into a big black hole will experience the same thing. For one thing, because of the extreme curvature of spacetime (so curved it is, in fact, closed- that's kind of the point of a black hole) every direction that the smaller black hole observes is towards the other black hole. That's one way to view the inescapability of a black hole.
Now, from the point of view of a distant observer, as the event horizons of the black holes get closer and closer, things do seem to get really weird, but that's only because time as experienced by objects in the immediate neighborhood of the merger gets more and more stretched out compared to time as experienced by the distant observer. I can't stress enough that the weirdness ONLY arises when comparing two different points of view. Neither the distant observer nor the suicidal one going along for the ride with the black holes (Call him Dr. Strangelove) experiences anything other than seemingly normal time*.
According to the distant observer, the spiraling black holes will drag spacetime around with them. You can imagine a grid of lines drawn on a sheet of rubber or taffy. Because spacetime has to be "smooth" in the calculus sense, the non-constant motion of the black holes around each must be transmitted outwards, sort of like waves on your rubber grid. This is called gravitational radiation.
Things will appear strange to the distant observer as the event horizons approach each other. Since Dr. Strangelove's time appears to stretch all the way out to infinity, it is tempting to imagine that the distant observer will see a normal image of him, just waving in slow motion like the bullet time special effects from the Matrix series of movies. That misses an important part! Since all aspects of Dr. Strangelove's time are seeming to slow down relative to us, the photons he emits as he waves backwards get farther and farther apart, and also get stretched out so that initially blue photons become green, then yellow, orange, red, infrared, radio, etc. So as Dr. Strangelove approaches the black hole, the most pronounced weirdness we see is not actually the slowing down, directly, but rather fading out, getting dimmer and redder.
Likewise, if we could see the spacetime around the merger directly, we would see the ripples fade out to "red" as well. In a finite time, even according to the distant observer, we would see all the action and details fade out to red while slowing down, leaving only the single, merged black hole.
*OK, technically, if Dr. Strangelove is a finite size, then his head and feet will have different experiences, but that's beyond the scope of this inquiry.
EDIT: By the way, the gravitational field can have mono- and dipole moments, but gravitational radiation is quadrupole.Tweet