Black Holes Have Only Two Parameters, but How They Form Is Still a Mystery
Gravitational waves and the EHT confirm that black holes really do have only two parameters, but how a 120-solar-mass black hole forms, whether dark matter is made of tiny black holes, and how the last parsec gets crossed all remain unsolved.
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The argument · tap a timestamp to hear it
Observers and theorists are not talking about the same black hole
Faced with the same object, observers treat it as nothing more than a heavy, dark point mass, useful for explaining the gravitational interaction with nearby matter; theorists treat it as a special geometry in which spacetime is curved so severely that time stops at the event horizon. The two definitions push research in opposite directions: observers extrapolate outward, theorists zoom in on structure at small scales. That split governs every later argument about how we prove that what we are looking at is a black hole.
— Vitor CardosoTrillions of black holes across the universe differ by only two parameters
A stationary Kerr black hole in vacuum is fixed entirely by two parameters, mass and spin, and every one of the trillions of black holes in the universe is the same in that respect; charge is allowed in theory, but the universe neutralizes it. The theorem, however, rests on two assumptions, vacuum and stationarity, and the real universe contains matter and changes over time. Cardoso's work consists precisely of breaking those assumptions and asking whether a black hole's radiation and dynamics change as a result.
— Vitor CardosoThat horizons always hide singularities is still only a conjecture
If the Earth suddenly collapsed into a black hole, it would be spinning too fast for a horizon to form at all; the equations return a naked singularity, and we have no theory for collapse without the shelter of a horizon. Cosmic censorship asserts that singularities are always hidden behind a horizon, but it is only a conjecture, and in theories of gravity in higher-dimensional spacetimes it already fails. Physicists still do not know whether it is correct.
— Vitor CardosoA black hole of 120 solar masses should not exist at all
Gravitational wave observations reach up to 120 solar masses, but that mass range is very hard to produce: stars above 80 solar masses become unstable and tend to blow apart rather than collapse, and the alternative route, merging first and growing afterward, does not work either because the black holes involved are too small and too unlikely to meet. Meanwhile every galaxy has a supermassive black hole of a million to a billion solar masses at its center, yet for the intermediate-mass black holes in between there is only scattered evidence.
— Vitor CardosoExplaining dark matter with black holes is too good to be true
Explaining dark matter with black holes requires specifying a mass first. Too heavy, and microlensing would have exposed them, which observations have not; too light, and Hawking radiation would have evaporated them long before today. Microlensing has already ruled out most of the parameter space, leaving only a narrow corner. Cardoso's judgment: possible, but unlikely. He calls the explanation "too good to be true, a bit of a long shot."
— Vitor CardosoNinety percent of that EHT picture was not measured
What the Event Horizon Telescope photographed is not the event horizon but the light ring, the innermost orbit on which photons can circle. More importantly, the images of M87 and the galactic center are extremely blurry: actual measurement accounts for only about 10%, while the other 90% comes from prior knowledge based on more than ten thousand simulations of the matter around a black hole. Cardoso's ideal future is an instrument with enough resolution that reconstruction from priors is no longer needed.
— Vitor CardosoSeeing lower-frequency signals means stretching the arms to a million kilometers
After LIGO, KAGRA is already running, and around 2030 India will join as well; Europe is planning the Einstein Telescope, a ground-based, upgraded version of LIGO, while Europe and the US are pushing to get LISA into space. LISA stretches the interferometer arms from LIGO's 4 kilometers to roughly 1 million kilometers, reaching signals at lower frequencies than the 20 hertz to 1 kilohertz band, with supermassive black hole mergers and even the inhomogeneities of the universe's earliest moments as the targets.
— Vitor CardosoA hydrogen atom may grow around a spinning black hole
A spinning black hole can amplify a low-frequency incoming wave and bounce it back; if the wave has mass, escape fails, it falls back in and is amplified again, producing a "black hole bomb." The axion has mass and is very light, so the theory predicts that if dark matter is made of axions, a cloud of them condenses around a spinning black hole, in a structure like a hydrogen atom: the nucleus is the spinning black hole, the cloud is the axions. This model shows up again and again in Cardoso's calculations.
— Vitor CardosoIn their own words · checked verbatim
But if you ask somebody a bit more like me, who works on theory and is interested in the fundamental concepts, then a black hole is a very different beast. It's an object that curves spacetime to the extent that time stops at the event horizon.
Vitor Cardoso3:07
Any black hole in the universe. That means of all the trillions of black holes we think are out there, all of them are specified entirely by just two parameters.
Vitor Cardoso10:47
If our planet, the Earth, would suddenly decide to collapse to a black hole and everything that composes the Earth would fall onto the black hole, it could not be a black hole because it's spinning too fast. And what the equations would tell us is there would be no horizon.
Vitor Cardoso19:34
We see black holes exist all the way up to 120 solar masses. We don't really know how they form.
Vitor Cardoso20:52
So if they were under the form of black holes, once in a while, micro black holes, one of these black holes would pass in front of a star, and it would lens the light from that star, so we would see the light from that star changing. And we haven't seen this.
Vitor Cardoso28:59
they're reconstructed from, I would say, roughly 10%. So 90% of the image is reconstructed, and it's reconstructed based on thousands of simulations that we do of matter around black holes.
Vitor Cardoso37:15
Gravitational waves are not traveling at the speed of light. So I'm always expecting some news along that side of things. So I always get a bit not depressed, but okay, it's the speed of light with 15 decimal digits.
Vitor Cardoso40:57
It's a fascinating thing to think that if dark matter would come under the form of axions, there might be systems there that look like atoms: a nucleus, which is a spinning black hole, surrounded by a cloud, like the hydrogen atom, a cloud of axions.
Vitor Cardoso1:00:37
Figures
| Parameters that fix all properties of a black hole | 2 (mass and spin) | 10:47 |
| Largest stellar-mass black hole observed | 120 solar masses | 20:52 |
| Mass threshold for stellar instability | above 80 solar masses | 22:33 |
| LIGO interferometer arm length | 4 kilometers | 42:38 |
| LISA interferometer arm length | roughly 1 million kilometers | 42:38 |
| Reconstructed fraction of the EHT image | about 90% | 37:15 |
| Arrival time difference between gravitational wave and light signal (GW170817) | 1.4 seconds | 40:57 |
| Photon counterparts observed in binary black hole mergers | never seen (out of two to three hundred mergers already seen) | 38:17 |
Glossary
- no-hair theorem
- A stationary black hole in vacuum is fixed by mass, spin (and charge) alone, with no other degrees of freedom.
- Kerr metric
- The exact general-relativistic solution describing the spacetime outside a rotating black hole.
- light ring
- The innermost orbit on which photons can circle a black hole, setting the shape of its shadow.
- cosmic censorship
- The conjecture that physical singularities are always hidden behind an event horizon, so naked singularities never appear in nature.
- matched filtering
- Comparing theoretical waveform templates against detector output to pull a gravitational wave signal out of noise.
- last parsec problem
- Once two supermassive black holes close to about 1 parsec, no mechanism is known to bring them together, which contradicts observations.
How to listen
Researchers and engineers working on gravitational waves, black holes or cosmology, plus science enthusiasts who want to hear how a working theorist checks the black hole concept against data.
Listeners already comfortable with the basic concepts can skip the opening definitions and start at 10:47, at the no-hair theorem.