On 14 September 2015 two black holes, about 36 and 31 times the mass of the Sun, merged 1.3 billion light-years away. For the last tenth of a second they circled each other hundreds of times a second, and the space around them carried the motion outward as waves. The lines on the stage are those waves in the plane of the orbit, crest after crest, tightening as the orbit shrinks, then a single ringing after the merger. Below is what LIGO actually recorded at Hanford and Livingston, and the sound of it.
Hear it plays the chirp once at its true speed while the stage runs in real time. At true pitch most of it lies between 35 and 250 Hz, below what phone speakers reproduce; two octaves up plays it four times faster. Moving a mass slider switches to the simple formula for your own binary.
Two waveforms. Full physics uses the numerical-relativity waveform that LIGO published with the discovery: Einstein's equations solved on a supercomputer for black holes of these masses. Simple formula is what you can do by hand: the leading-order chirp from the guide, where the time left before merger is τ = (5/256)(G𝓜/c³)−5/3(πf)−8/3 and 𝓜 is the chirp mass, then a ringing at the frequency and damping time of the final black hole (fits by Berti and colleagues, final spin from Rezzolla and colleagues, energy radiated from a standard fit), joined by a smooth bridge. The bridge is our choice, not physics.
The test against the data. The page takes LIGO's Hanford recording, divides out the detector's noise spectrum (whitening) and keeps 35–350 Hz. It processes the chosen waveform the same way, slides it in time and phase, and reports the best normalised overlap: 1 would be a perfect copy, and stretches of pure noise score about 0.17 (0.22 at most in 22 trials). The full-physics waveform reaches 0.76. The simple formula stays near 0.3 whatever masses you choose: it is right about the early chirp but falls many cycles behind in the last orbits, which is why gravitational-wave astronomy needs numerical relativity. Livingston recorded the same signal flipped in sign, because its arms are rotated relative to Hanford's, and earlier; the page finds the delay by the same sliding test.
The picture. The stage is the orbital plane, seen from above, at true scale in kilometres in the source's own time. Each point shows the wave that left the binary r/c earlier: h ∝ A(t − r/c)·cos(2Φ(t − r/c) − 2φ), so crests form two spiral arms. Lines are drawn along the crests and between them; brightness is the wave's amplitude with the 1/r fall-off removed so the outer waves stay visible. Near the binary, within about a sixth of a wavelength, the wave picture does not apply and the lines fade. Black holes are drawn at their Schwarzschild radius, 2.95 km per solar mass, with separation from Kepler's law at the current frequency.
Distance and redshift. Masses are given as at the source. The waves stretch on their way here, so the detector sees every frequency lower and every duration longer by (1 + z); z comes from the distance in a flat universe with H₀ = 67.7 km/s/Mpc and Ωm = 0.31. Strain at Earth is for a binary seen face-on, the most favourable orientation.
A study in the language of light as structure: fine white lines on black, one flash at the climax, then quiet rings moving out of the frame. It recreates no specific work.