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Frank Wilczek

If mature black holes had personalities, they would be extremely introverted. They don’t let anything out – not light, not particles, and certainly not music.
Hawking radiation is a fascinating exception to this rule, but for astrophysical black holes, it is a tiny effect.
But before they settle down, during their brief but wild youth, newly formed black holes ring out a strange, pure music. It would be beautiful to experience, and soon we will be able to do it.
When a new black hole is formed, say by collapse of a star or by fusion of other objects such as neutron stars or smaller black holes, the material that produced it gets swallowed up. Once that material passes beyond the newly formed event horizon, no trace of it remains perceptible.
The baby black hole itself, as a distortion of space-time, quickly settles into a stable shape, sculpted by its own gravity. The same force that makes stars and planets very nearly into round balls – or, if they’re spinning, smooth ellipsoids – works even more powerfully to mould black holes.
Precisely because they swallow all signs of their origin and squash any outer lumpiness, black holes reach a level of mathematical perfection that is unique among macroscopic objects. Given only a black hole’s mass and angular momentum, the equations of general relativity predict with utter precision the distortion of space-time it embodies.
But the static perfection into which black holes settle is only part of their story, and not the most interesting part.


Consider, for example, a baby black hole born from the merger of two parent black holes that were orbiting one another. The baby starts out as a dumbbell-shaped fusion of the two parent bodies, connected by a thin neck. In the process of sculpting that lopsided, wobbly baby into the sort of stable, “perfect” adult as described above, gravity has a lot of work to do. Its tinkering with space-time sends out ripples – gravitational waves – that eventually make their way towards Earth, where we can detect them.
The earliest stages of this settling process are fast, violent and complicated. They are like the initial clang of a struck bell, or the initial splash of a plunging stone. But the longer, calmer stage that follows is more musical. Here are some programme notes to help you enjoy the coming concert.
The sounds that we hear with our ears after a bell is struck are vibrations in air. The waves that we see with our eyes after a stone plunges into a still lake are fundamentally similar kinds of vibrations, but moving through water.
The waves that a baby black hole emits are much the same, but they are disturbances in space-time itself rather than air or water. Such waves of space-time distortion are called gravitational waves. “Empty space”, rather than air or water, is the medium that supports gravitational waves. Thus, “empty space” is not a void.
Gravitational waves spread out from their source and travel at the speed of light over vast distances. Typical sources are very far away, so by the time the gravitational waves they generate reach Earth, their energy has been diluted over a large volume. As a result, the distortions they produce in our neighbourhood are tiny.
Though the theoretical existence of gravitational waves was widely appreciated for decades, they were first detected in 2015. That pioneering detection was the culmination of a heroic effort by the Laser Interferometrer Gravitational-wave Observatory (Ligo) collaboration.
The challenge they overcame was to sense distortions of distance at the level of a part in 10 to the power of minus 22.
These are tiny changes indeed. They translate, for their four-mile-long (6.4km) instruments, to subatomic – in fact, subnuclear – distances. To reach that sensitivity, they invented several new measurement and noise suppression technologies.
Such tiny magnitudes are difficult to comprehend, so another perspective might be helpful. Translated into time, distortions of this size would represent about a thousandth of a second over the lifetime of the universe. Remarkably, people are closing in on the goal of making clocks that are that accurate. An array of such clocks would give us another way to observe gravitational waves, now through their distortion of time.
Today more than a dozen second-generation projects are under construction around the world. They incorporate new ideas and refinements. People are also actively exploring the possibility of putting gravitational wave detectors in space, where there is less noise and more room to expand. China’s ambitious Taiji programme aims in that direction.
This ferment of innovation and investment will allow scientists to perceive incoming gravitational waves much more fully. They will be able to hear, together with the loud clangs that announce the moment of merger, the quieter but more musical tones that follow.


During the “ring-down” stage, the newly formed black hole is close to maturity, but still shows signs of adolescence. With an overabundance of energy, it rocks and rolls.
Switching metaphors, the teenage black hole is like a vibrating bell. It is close to its final shape, but on top of that it vibrates. These vibrations have the wonderful name “quasi-normal modes”.
What are quasi-normal modes? To answer that, I should first explain that normal modes are idealised, perfectly periodic – or pure tone – vibration patterns of systems that do not lose energy. A bell that vibrates in a vacuum cannot emit sound waves, so its vibrations retain their strength; in this case normal modes are close to the truth of vibration.
Still, there are also other, generally less efficient ways to share the vibrational energy, such as heating up the bell. But it turns out to be very convenient, mathematically, to calculate idealised vibration patterns that are self-contained and last forever. Those are the “normal” normal modes. Normal modes are the bread and butter of elementary, intermediate and even most advanced physics courses.
On the other hand, it is quite possible to get a PhD in physics without ever encountering quasi-normal modes.
Quasi-normal modes are what you get when you bring in more realism by allowing for the effect of radiation – for example, sound waves for bells, or gravitational waves for black holes. Engineers usually meet quasi-normal modes much earlier in their education.
Including energy loss complicates the mathematics but brings it closer to reality. Most importantly, it makes the vibrations decay over time. Normal modes are forever, but quasi-normal modes, like the tones of real bells, die away.
For black holes, normal modes are not a good option because, in this context, it is hard to separate the gravitational forces that make space-time vibrate from the gravitational forces that make it radiate. We need to deal with quasi-normal modes from the start.
State-of-the-art calculations require partnering with supercomputers. A recent high-level review of the subject had 68 authors, 1,587 references, and 269 pages of dense, equation-heavy text. The exhilarating prospect of comparing beautiful, intricate mathematics with beautiful, intricate observations motivates an enthusiastic, hard-working international community of scientists.
A very new frontier of investigation is the effect of quantum mechanics on gravitational radiation. It’s early days yet, but I’m optimistic that here we will realise a dream of modern physics, by observing quantum fluctuations in space-time itself.
Why should we care about black hole bells? After all, there are many other musical instruments that make more accessible sounds more easily, and we can tune them, improve them, or even invent new ones. Black hole bells are an inspiring challenge, in part, precisely because they can’t be tinkered with. They are what they are, and that fact gives us interesting, challenging work to do, both to sense them and to understand them.
Black hole bells are a gift from nature that it would be shamefully ungrateful to refuse. Ideas like “celestial harmony” and “music of the spheres” have reflected human reverence and bliss since ancient times. Perhaps nowhere else are those ideas embodied so clearly.


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Newly formed black holes ring out a strange, pure music, and soon we may be able to experience it


Newly formed black holes ring out a strange, pure music, and soon we may be able to experience it.


Expresses the views, ideas and conclusions of the author. (Eg. Enough of Crazy Rich Asians, think of crazy poor Hongkongers.)


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Wilczek’s Multiverse

Good vibrations: the music of black holes

.css-1c6uqr6{color:inherit;font-weight:inherit;font-size:inherit;font-family:inherit;line-height:inherit;overflow-wrap:break-word;}Newly formed black holes ring out a strange, pure music, and soon we may be able to experience it

Newly formed black holes ring out a strange, pure music, and soon we may be able to experience it