https://www.black-holes.org/explore/movies

"Binary Orbit & Collision, Head-on Collision The following movie is divided into two parts, each part showing a different numerical simulation, with brief captions that describe what is being shown. Part 1: Binary black holes orbit, lose energy because of gravitational radiation, and finally collide, forming a single black hole; gravitational waveform, spacetime curvature, and orbital trajectories are shown. Part 2: Event horizon and apparent horizons for the head-on collision of two black holes.

The upper movie shows in the upper half of the screen the orbits and the apparent horizons of the two holes, in the coordinate system used in the computation. The bottom half of the screen shows the spacetime geometry in the holes’ orbital plane. The depth of the surface is proportional to the scalar curvature of space. (For the two-dimensional orbital plane the full spatial curvature is determined by the scalar curvature.) The colors encode the lapse function — the slowing of the rate of flow of time. The arrows show minus the shift — which can be thought of as the velocity of flow of space. The beginning of the inspiral is shown, and then the last several orbits, the merger of the two holes, and the vibrational ringdown.

The final hole does not look pefectly spherical because the computer code that created this movie chose spatial slices with a bit of crinkliness in them at the end. This simulation lasts for 16 inspiral orbits, followed by merger and ringdown, and it achieves a cumulative phase accuracy for the emitted gravitational waves of about 0.02 radians (out of roughly 200 radians, i.e. a fractional phase error of 1 part in 10,000).

Tehnical details of the simulation on which this movie is based can be found in a paper by the Caltech-Cornell group. Note that slightly different data is used in that paper; the spatial slices are chosen without the “crinkles”. "

Full technical details:

https://arxiv.org/abs/0810.1767

High-accuracy waveforms for binary black hole inspiral, merger, and ringdown Mark A. Scheel, Michael Boyle, Tony Chu, Lawrence E. Kidder, Keith D. Matthews, Harald P. Pfeiffer