Spacetime and the cosmos
14 September 2015
Hearing black holes merge
LIGO and Virgo collaborations
Can you hear space itself stretch?
Two black holes, about 1.3 billion light-years away, spiralled together and merged. The ripple in spacetime stretched LIGO’s 4-km arms by far less than the width of a proton. The new black hole then rang down like a struck bell.
First, make a guess
A heavier black hole rings…
- Real frequency
- 195 Hz
- Fades to a third in
- 3.4 ms
- Swings before it fades
- 0.7
- Damping ratio ζ
- 0.232
A non-spinning black hole’s pole can only slide along one line: its mass sets both pitch and fade together. It dies out in under one swing. Sound is shifted into hearing range: its pitch follows the pole’s height and its fade follows the pole’s distance from the line.
How they figured it out
Einstein predicted gravitational waves in 1916 but thought they would be far too weak ever to detect. In 1972 Rainer Weiss, setting a class exercise at MIT, worked out how a laser interferometer could do it, and listed every source of noise that would get in the way.
It took over forty years of engineering. The upgraded detectors had barely been switched on when, on 14 September 2015, a signal arrived: a fifth of a second long, chirping upwards from about 35 to 250 Hz. Two black holes had merged 1.3 billion years ago. Weiss, Kip Thorne and Barry Barish shared the 2017 Nobel Prize.
The equation
After the merger, the signal is a single tone fading fast: the black hole ringing.
See it in real life
The chirp
Shifted into sound, the signal is a short rising “whoop”, like a bird’s chirp. Tap a bowl of jelly and a wobble runs through it, then dies away. Space did the same: it rang and settled, and the ringing faded in a few thousandths of a second.
Where engineers use it
Vibration isolation
LIGO’s mirrors hang from multi-stage pendulums: some of the best vibration isolation ever engineered.
Matched filtering
Signals are found by comparing data with templates, as radar and mobile phones do.
Where it came from
- General relativity November 1915
Led to
Einstein predicted gravitational waves in 1916; it took a century to detect them.
- The first black hole solution 1916
Led to
LIGO’s signal came from two black holes merging into one.
- Light is electromagnetism 1865
Analogy only
Gravitational waves travel at the speed of light, like Maxwell’s light waves.
Where the comparison stops: Light is a wave in electric and magnetic fields. Gravitational waves stretch space itself, and are far, far weaker.
- Laplace transform and poles 1812
Same technique
A ringing black hole is described by complex frequencies, like poles: pitch and fade in one number.
Where the comparison stops: The black hole’s frequencies come from Einstein’s equations, not from a circuit or spring, and only the late ringdown looks like this.