Black holes
Gravity so strong that light cannot escape. Everything here is ray traced live from Einstein's equations: squeeze the Sun into a black hole, bend starlight round it, slow a clock at its edge and watch it tear a star apart.
Above, every pixel is a ray of light followed back from your screen through the curved space round a black hole, step by step, on the Schwarzschild solution of Einstein's equations. The disk's far side shows over the top because its light bends round. Each section below takes one idea and lets you push it. Distances are in rs, the radius of the event horizon.
Squeeze the Sun into a black hole
The idea
Anything becomes a black hole if it is squeezed small enough. For the Sun that means a ball 2.95 km in radius1. At that size, getting away from its surface would take the speed of light itself.
In plain words
As the Sun shrinks, gravity at its surface grows, and so does the speed needed to escape it. Light climbing out loses energy and arrives redder. Near the end the light bends round the edge, so you see more than half the surface at once. At 2.95 km the escape speed reaches light's and the star goes dark. The surface has become an event horizon.
The numbers
The radius is 2GM/c², the Schwarzschild radius, and it grows in step with mass: 8.87 mm for the Earth's mass2, 2.95 km for the Sun's, and 12.7 million km for the 4.3 million Suns at the centre of our galaxy3.
Where the idea came from
In 1783 John Michell worked out that a star 500 times the Sun's radius, with the Sun's density, would hold back its own light4. In December 1915, weeks after Einstein gave his theory its final form, Karl Schwarzschild found its exact solution round a mass and sent it to Einstein from the Russian front, where he was serving in the German army56.
Try it
Slide all the way. In the last few kilometres the light reddens, fades and is gone.
Light can orbit a black hole
The idea
Light passing a black hole bends, and at one and a half times the horizon's radius it can travel in a circle. Light aimed closer than 2.6 horizon radii from the centre never gets out7.
Why it looks bigger
Every line of sight aimed within 2.6 rs of the centre ends on the horizon, so a black hole casts a shadow 2.6 times the horizon's width. Light can circle at the photon sphere, but only balanced on a knife edge: the slightest nudge sends it in or out.
Try it
Slide the aim towards 2.6 rs. Just outside it the light goes round more and more times before it escapes.
A black hole bends the whole sky
The idea
A black hole is a lens. Light from the stars behind it bends round both sides, so each star shows twice, and a star exactly behind it spreads into a ring, an Einstein ring.
Reading the picture
The bright star in the middle of the frame shows twice: once outside the ring on its own side, and fainter inside it on the far side. Drag to fly round the hole and watch the stars slide round its edge. The Sun bends starlight the same way, by 1.75″ at its edge11.
The numbers
Seen from 24 rs away, as here, the ring is 18° from the centre and the shadow 12° across. Light skimming the photon sphere can go round the hole any number of times, so a thin copy of the whole sky lies just outside the shadow.
See it in 3D
The same bending, a million times weaker, measured at the 1919 eclipse.
The disk wraps over the top
The idea
Gas falling into a black hole spins into a flat disk. Its light bends round the hole, so from almost any angle you see the far side of the disk standing up over the shadow, and its underside below it.
What you are seeing
The band across the middle is the near side of the disk. The arch over the top is the far side, whose light climbs over the hole to reach you, and the thinner arch below is its underside. The faint ring hugging the shadow is light that went once round the hole first.
Where the picture came from
Jean-Pierre Luminet calculated the first image of a black hole with a disk in 1979 on an IBM 7040 and drew it by hand from the numbers, a dot of Indian ink at a time1415. The black hole in Interstellar (2014) was rendered from the same physics by Kip Thorne and the film's effects team16.
What is drawn
The disk runs from 3 rs, the innermost stable orbit8, out to 13 rs, hottest just outside its inner edge, as in the standard thin-disk model. Real disks are far hotter and shine mostly in ultraviolet and X-rays; this one is coloured as if it glowed in visible light.
Try it
Press Gravity off: the disk falls flat into an ellipse and the hole shrinks to a black ball. That is how far the bending reaches.
One side burns brighter
The idea
The inner edge of the disk orbits at half the speed of light. On the side coming towards you its light is squeezed bluer and thrown forward, and on the side going away it is stretched redder and dimmed.
The numbers
At the innermost stable orbit, 3 rs, gas moves at half light speed17. Head on, that makes its light 1.73 times bluer coming and 0.58 times going, and brightness goes as the fourth power of that shift, so the approaching side is up to 81 times brighter than the receding one. Climbing out from 3 rs, light also loses 18% of its energy to gravity.
How we know
The EHT's picture of M87* is brightest on one side, where the gas swings towards us, as the models of its disk predict9. The effect on a disk's light was worked out in the 1970s18, and Luminet's 1979 picture is brightest where the gas comes towards us14.
Switch them off
Turn the Doppler shift off and both sides match. Turn gravity's redshift off too and the inner disk shines at full strength, the way it would with no gravity to climb out of.
Clocks slow down near the edge
The idea
Time runs slower in stronger gravity. Seen from far away, a beacon hovering near a black hole flashes slowly and its light arrives redder. At the horizon both would stop.
The numbers
A clock hovering at r ticks at √(1 − rs/r) of the rate of one far away19: 82% at 3 rs, 30% at 1.1 rs and 10% at 1.01 rs. Its light is stretched by the same factor, so the beacon reddens and dims as it nears the edge.
How we know
The Earth does it too. In 1959 Pound and Rebka sent gamma rays up a 22.5 m tower at Harvard and found them shifted by the amount relativity predicts20; optical clocks now pick up the difference across 33 cm21, and GPS satellites correct for it every day22.
Falling in
Someone falling in feels nothing special at the horizon and crosses it in a short time by their own watch. A faraway watcher never sees them cross: their image slows, reddens and fades just outside.
Tides tear stars apart
The idea
A black hole pulls harder on the near side of anything than on the far side. Close in, that difference stretches a star into a long stream of gas. Astronomers call it spaghettification.
The numbers
Tides are fiercest round small black holes. At the horizon of one of 10 Suns, a person's feet would be pulled about 20 million g harder than their head; at the horizon of the 4.3 million Suns at our galaxy's centre, a ten-thousandth of a g. Above about a hundred million Suns, a star like the Sun crosses the horizon before tides can tear it2324.
How we know
In 2019 telescopes caught a star of about the Sun's mass being torn apart by a black hole of about a million Suns, just over 215 million light-years away. ESO called it the closest such flare recorded to date2526.
What the drawing shows
Half the star is flung away. The rest falls back, circles the hole and heats up, which is the flare telescopes see. Each particle follows Newton's gravity, which is close enough this far from the horizon.
The black hole at the centre of our galaxy
The idea
At the centre of the Milky Way, 27,000 light-years away, stars swing round something with 4.3 million times the Sun's mass that gives out no light of its own. Thirty years of following their orbits weighed it.
The numbers
The star S2 goes round every 16 years. At its closest, in May 2018, it passed 120 AU from the centre at 7,650 km/s, 2.55% of light speed27. The mass is 4.297 million Suns, at 8,277 parsecs3.
How we know
Andrea Ghez's team at the Keck telescopes and Reinhard Genzel's at ESO followed these stars from the 1990s, and shared the 2020 Nobel Prize in Physics "for the discovery of a supermassive compact object at the centre of our galaxy"28. In 2022 the EHT photographed its shadow10.
Why it must be a black hole
S2 swings round something that fits inside its closest pass, 120 AU, yet outweighs four million Suns and gives no light. Nothing else known can be that heavy, that small and that dark. The orbits are drawn from the fits in Gillessen et al. (2017)29.
A photograph of a shadow
The idea
In 2019 the Event Horizon Telescope showed the first picture of a black hole: the shadow of the one in the galaxy M87, 55 million light-years away, inside a ring of light bent round it. Seeing something that small takes a telescope the size of the Earth.
The numbers
The ring is 42 microarcseconds across, round a black hole of 6.5 billion Suns9. A dish D across sees detail as fine as the wavelength over D; at 1.3 mm, the EHT's longest baselines reach about 25 microarcseconds9.
How we know
Eight telescopes at six sites (Hawaii, Arizona, Mexico, Chile, Spain and the South Pole) watched M87* in April 2017 at 1.3 mm. Their recordings, timed by atomic clocks, were combined into one telescope as wide as the Earth9.
Our model beside it
Ours is a disk of gas glowing close to the hole, seen 17° from its axis as M87* is, blurred to the dish's resolution and coloured the way the EHT colours its pictures. The ring's size matches, and so does its bright side: gas coming towards us is beamed brighter9. The real gas is not a thin disk, which is why the details differ.
See it in 3D
The viewer's spinning black hole bends the real sky round itself.
Weighed, photographed, heard
A century ago black holes were a curiosity of the equations. Now astronomers weigh them by the stars round them, photograph their shadows9 and hear them merge39.
Questions
What is a black hole?
A region where gravity is so strong that nothing, light included, can get out. Its boundary is the event horizon, at 2GM/c² from the centre for one that does not spin: 2.95 km for every Sun's worth of mass130.
Would a black hole suck the Earth in?
No. Far from it, a black hole pulls like anything else of the same mass. If the Sun were swapped for a black hole of the same mass, the Earth would keep to the same orbit30.
What was the first black hole found?
Cygnus X-1, a black hole orbiting a blue supergiant star, identified in 1972 by two teams at once3132. It has 21 times the Sun's mass33.
How many black holes are there?
Astronomers estimate that 100 million roam among the stars of the Milky Way alone34.
What is the nearest black hole?
The nearest known is Gaia BH1, about 1,560 light-years away, found in 2022 from the wobble of the Sun-like star circling it35.
Do black holes last for ever?
Not quite. Stephen Hawking showed in 1974 that they should glow faintly and slowly lose mass36. One of the Sun's mass would glow at 60 billionths of a degree above absolute zero, colder than the 2.725 K of the cosmic microwave background3738, so today it takes in more than it gives out.
What happens if you fall in?
Into a small one, tides pull you apart before you reach the horizon. Into a giant one you cross the horizon without feeling it, and from then on every path leads to the centre. From outside, nobody ever sees you cross.
Sources
- IAU 2015 Resolution B3: the nominal solar mass parameter, GM = 1.3271244 × 10²⁰ m³/s²
- IERS Conventions (2010): the geocentric gravitational constant, GM = 3.986004418 × 10¹⁴ m³/s²
- GRAVITY Collaboration (2022), Mass distribution in the Galactic Center based on interferometric astrometry of multiple stellar orbits, Astronomy and Astrophysics 657, L12
- Michell, J. (1784), On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, Philosophical Transactions of the Royal Society 74, 35
- Schwarzschild, K. (1916), Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie, Sitzungsberichte der Preussischen Akademie der Wissenschaften 1916, 189 (English translation by Antoci and Loinger, 1999)
- Weinstein, G. (2012), From the Berlin "Entwurf" Field Equations to the Einstein Tensor II: November 1915 until March 1916 (Schwarzschild's letter to Einstein of 22 December 1915 from the Russian front, Collected Papers of Albert Einstein vol. 8, doc. 169)
- Synge, J. L. (1966), The Escape of Photons from Gravitationally Intense Stars, Monthly Notices of the Royal Astronomical Society 131, 463
- Bardeen, J. M., Press, W. H. and Teukolsky, S. A. (1972), Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation, The Astrophysical Journal 178, 347
- Event Horizon Telescope Collaboration (2019), First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, ApJ Letters 875, L1
- Event Horizon Telescope Collaboration (2022), First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way, ApJ Letters 930, L12
- Dyson, F. W., Eddington, A. S. and Davidson, C. (1920), A Determination of the Deflection of Light by the Sun's Gravitational Field, Philosophical Transactions of the Royal Society A 220, 291
- Einstein, A. (1936), Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science 84, 506
- Hewitt, J. N. et al. (1988), Unusual radio source MG1131+0456: a possible Einstein ring, Nature 333, 537
- Luminet, J.-P. (1979), Image of a spherical black hole with thin accretion disk, Astronomy and Astrophysics 75, 228
- Luminet, J.-P. (2019), An Illustrated History of Black Hole Imaging: Personal Recollections (1972-2002)
- James, O., von Tunzelmann, E., Franklin, P. and Thorne, K. S. (2015), Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar, Classical and Quantum Gravity 32, 065001
- Fabian, A. C. and Lasenby, A. N. (2019), Astrophysical Black Holes (eq. 7.11: half the speed of light at the innermost stable circular orbit)
- Cunningham, C. T. (1975), The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole, The Astrophysical Journal 202, 788
- Gravitational time dilation outside a spherical, non-rotating mass
- Pound, R. V. and Rebka, G. A. (1960), Apparent Weight of Photons, Physical Review Letters 4, 337
- Chou, C. W., Hume, D. B., Rosenband, T. and Wineland, D. J. (2010), Optical Clocks and Relativity, Science 329, 1630
- Ashby, N. (2003), Relativity in the Global Positioning System, Living Reviews in Relativity 6, 1
- Hills, J. G. (1975), Possible power source of Seyfert galaxies and QSOs, Nature 254, 295
- Gezari, S. (2021), Tidal Disruption Events, Annual Review of Astronomy and Astrophysics 59, 21
- ESO (2020), Death by Spaghettification: ESO Telescopes Record Last Moments of Star Devoured by a Black Hole (eso2018)
- Nicholl, M. et al. (2020), An outflow powers the optical rise of the nearby, fast-evolving tidal disruption event AT2019qiz, Monthly Notices of the Royal Astronomical Society 499, 482
- GRAVITY Collaboration (2018), Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole, Astronomy and Astrophysics 615, L15
- The Nobel Prize in Physics 2020
- Gillessen, S. et al. (2017), An Update on Monitoring Stellar Orbits in the Galactic Center, The Astrophysical Journal 837, 30
- NASA Goddard, Imagine the Universe!: Black Holes
- Webster, B. L. and Murdin, P. (1972), Cygnus X-1: a Spectroscopic Binary with a Heavy Companion?, Nature 235, 37
- Bolton, C. T. (1972), Identification of Cygnus X-1 with HDE 226868, Nature 235, 271
- Miller-Jones, J. C. A. et al. (2021), Cygnus X-1 contains a 21-solar mass black hole: Implications for massive star winds, Science 371, 1046
- NASA (2022), Hubble Determines Mass of Isolated Black Hole Roaming Our Milky Way Galaxy
- El-Badry, K. et al. (2023), A Sun-like star orbiting a black hole, Monthly Notices of the Royal Astronomical Society 518, 1057
- Hawking, S. W. (1974), Black hole explosions?, Nature 248, 30
- Hawking, S. W. (1975), Particle creation by black holes, Communications in Mathematical Physics 43, 199
- Fixsen, D. J. (2009), The Temperature of the Cosmic Microwave Background, The Astrophysical Journal 707, 916
- Abbott, B. P. et al. (2016), Observation of Gravitational Waves from a Binary Black Hole Merger, Physical Review Letters 116, 061102
- ESO: the first image of a black hole, M87* (eso1907a), EHT Collaboration, CC BY 4.0
- NASA/Goddard Space Flight Center Scientific Visualization Studio, Deep Star Maps 2020 (Gaia DR2: ESA/Gaia/DPAC)
The ray traced scenes follow each pixel's light back along its path in Schwarzschild spacetime (a black hole that does not spin), integrated in steps; the readouts run on the formulas they quote. The disk is a thin disk coloured as if it glowed at visible temperatures, and its grain is drawn. The stars are drawn too; the Milky Way behind them is NASA's Deep Star Maps 2020. The star torn apart is drawn larger than life when its readout says so. The EHT's picture is by the EHT Collaboration (CC BY 4.0).