Merger of two black holes, one much bigger than the other
 
The motion of a black hole as it orbits around, and eventually falls into, a much bigger black hole. Tell me more! The grey surfaces are the horizons of the black holes, what you could think of as their surfaces, though there isn't anything solid there. The big hole has 3,000 times our sun's mass, and is about 8,000 miles across. The larger hole is spinning very rapidly (this is why its equator bulges out). The small hole has the mass of a neutron star (about one and a half time our sun's mass). The motion is shown at its natural speed, is drawn accurately, and has a thirty second tail. The big hole is drawn to scale relative to the motion. The small hole is blown up about 100 times in size so that you can see where it is. The little black hole really would deform the big black hole's horizon, but the deformations shown here are a fictional exaggeration. To get what you see here, I added a deformation that scales with the cube of the distance, and then I cranked up its strength until I could see it. So in short, the motion is fairly realistic but the deformation of the horizon is dramatized.
Are these the same as the LIGO ones? Yes and no. Yes, these are two black holes, but no, they are pretty different from the holes that LIGO saw. Here's a simulation of LIGO's first direction (this beautiful work by the SXS collaboration is not mine):
There are two main differences between this simulation and mine. The first is that this one shows in glorious detail how the holes would distort the appearance of objects behind them (an effect called gravitational lensing). I didn't include gravitational lensing in my simulations, though I would love to (help me students!). The other difference is that the two holes that LIGO saw were similar in size, making for a more violent merger. In my simulations, the companion hole is so small that it hardly bothers the big one. Show me another one!
This time, the big hole is 3 million times as massive as our sun! The small one is also bigger (90 solar masses) but it is now wildly small compared to the big one. Showing this one in real time would take a few months. I've sped it up to last just a minute or so. The larger black hole is again spinning very fast, at 90% of the rate thought to be physically possible. However, this time I don't show any bulge on the big black hole due to the (now puny) small hole. The big hole is about half of a lightminute in size, and it is drawn to scale with the curves which show the previous twelve hours worth of motion. What am I hearing? The motion makes gravitational waves, and you are hearing the waves played as sound (also sped up to last seconds instead of months). The waves have a rich spectrum with many lines (frequencies) at harmonic combinations of three fundamental frequencies. During the pretty or simple bits, a whole lot of the lines briefly overlap (because the ratio of two of the fundamental frequencies becomes a rational number). You can both see and hear this, since playing sound at two nearly equal frequencies causes "acoustic beats", a pulsing with frequency given by the difference of the two nearly equal frequencies. Tell me more! These movies were made using an approximation scheme taken from these two technical papers [1] [2]. The approximation works when the smaller object (1) is very compact, or has been squashed into a very small size and (2) is much less massive than the big black hole. The first condition is needed so that the smaller object will not be ripped apart by the strong tidal forces produced by the large black hole. In the ideal case that smaller object is just another black hole, but other compact objects would also survive. The second condition is more complicated. These events produce gravitational waves, a type of radiation predicted by Einstein's theory of gravity (called general relativity) in the early part of the 1900s. That second condition in the approximation is needed so that the motion of the small object is not violently disturbed by the waves that it is producing. As a result, for long stretches of time the small object moves along curves that are relatively easy to calculate. Those curves are Einstein's relativistic replacement for the familiar elliptical orbits of planets, a discovery made by Johannes Kepler around the year 1605. When two objects are especially close to each other, they actually don't move along ellipses at all. Although general relativity was the first widely accepted theory that could explain the correct shapes traced out by objects that are very near each other, those shapes were still pretty close to ellipses. It is only when the two objects are squashed into such small sizes as black holes that they can get near enough to trace out the wildly more complex curves, or "orbits", seen in these movies. We have not yet observed such dramatic orbits, but since general relativity has been so successful in every case where it could be tested, there is little doubt that these orbits exist in nature. Although these orbits are relatively easy to calculate, they look like a tangled mess throughout most of the merger process. Occasionally though, conditions become just right for the orbits to take on a more beautiful form called a resonance. You can see those in the previous movie, but also in this older one (before I knew how to do high resolution on youtube) that pauses at a couple of resonances to fly the camera around so that you can see the orbit from different perspectives. During the pauses, a red arrow is drawn along the rotation axis of the large black hole to help keep you oriented.
Here are some still images comparing resonant and ordinary orbits.
Finally, gravitational waves are really the whole reason for making these simulations. The LIGO detector that first observed gravitational waves in September of 2015 could detect something like the lighter pair of black holes above, but not the heavier pair. The waves from the heavier pair are at too low of a frequency for LIGO. That said, they could be observed by future detectors in space (about a million times larger than LIGO). Background information The numerical calculations that went into these movies were done by Steve Drasco and Curt Cutler. We used our own implementations of the GairGlampedakis kludge (PRD 73 064037 or grqc/0510129) and the Babak et al quadrupoleoctupole waveform approximation (PRD 75 024005 or grqc/0607007). The simulations and the rendering of the still images were done with Matlab. The simulations are quick, a couple of minutes on a laptop. The rendering of the movie frames takes longer, a few hours on a laptop at high resolution. The frames were stitched together into a movie using QuickTime 7 Pro. Do you have more movies like this? Yes, you can find some at my youtube channel, but I also have some older ones for download, they have different masses, frequencies, colors, etc. As with any of the things on this website, if you aren't using them to make money in some way, then please do download them, and please do show them to as many people as you like, so long as you credit me. If you want to use them in something that's intended to make money, we'll need to talk to discuss licensing before you can use them. 250 solar mass hole with an eccentric 1.4 solar mass black hole (33 sec, 4 MB) [different initial conditions and spin (10 sec, 9 MB)] 3000 solar mass hole with a 1.4 solar mass black hole (48 sec, 15 MB) [fast enough to be heard (5 sec, 12 MB) ] 100 solar mass hole with 1.4 solar mass black hole, in real time (34 sec, 12 MB) [the same but nearly circular (31 sec, 12 MB)] 3 million solar mass hole with 90 solar mass hole (3 min, 78 MB) 3 million solar mass hole with 270 solar mass hole (1 min, 26 MB) [(without axes 1280 x 720, 24 MB), (with axes 1280 x 720, 41 MB) ] 3 million solar mass hole with 540 solar mass hole (20 sec 21 MB)
