Gravity does not only pull on apples and planets. It bends the path of light. Put a black hole between Earth and a distant galaxy, and the galaxy's light reaches our telescopes along several bent paths at once: we see arcs, two copies, or, at perfect alignment, a closed circle of light called an Einstein ring. Fly in close and the bending turns extreme: the black hole wears its own glowing disk like a halo.
Can gravity bend light?
Yes, and it was the first famous test of Einstein's general relativity. Mass curves spacetime, and light follows the curve. A ray grazing the Sun is deflected by 1.75″ (arcseconds), twice the 0.875″ a Newtonian "light falls too" argument gives. On 29 May 1919 two British expeditions photographed stars around the eclipsed Sun, at Sobral in Brazil and on the island of Príncipe. The stars had shifted outward. Scaled to the Sun's edge: 1.98 ± 0.12″ at Sobral, 1.60 ± 0.31″ at Príncipe. Einstein became famous almost overnight. Today radio telescopes confirm the effect to about 0.01 %.
The angle is 2 rs/b: twice the Schwarzschild radius divided by the miss distance. For the Sun, rs is 3 km and b is 696 000 km, which is why the bend is so small. In the Side view an orange wedge marks that angle on each path, stretched about 77 000 times so you can see it; the true value is written beside it. A heavier hole bends harder: drag the Mass slider and watch the wedges open. The grid around the black hole is a drawing of curved space: its lines bunch toward the mass.
α̂ = 2 rs / b bending angle · rs = 2GM/c²Why does perfect alignment make a ring?
If a galaxy, a heavy mass and your telescope sit on one straight line, no side is special. Light passing the mass at the right distance, on every side at once, is bent into your telescope, and you see a circle: an Einstein ring. Its angular radius is θE = √(2 rs · DLS / (DL·DS)). For 3 × 10¹⁰ solar masses halfway to a galaxy at redshift 1, θE = 0.32″, and the rays pass 1.85 kiloparsecs from the mass, 640 000 times its Schwarzschild radius.
The black hole itself stays invisible. Lensing never changes a patch's surface brightness. It enlarges the patch, so the ring holds more light in total. Chwolson described rings in 1924 and Einstein in 1936, and Einstein doubted anyone would see one. The first, MG1131+0456, turned up in radio images in 1988.
θE = √( 2 rs · DLS / (DL DS) ) Einstein radius β = θ − θE² θ / |θ|² lens equation: where each sky pixel really looksWhy two images, arriving at different times?
Move the mass off the line and the ring breaks in two. One image sits outside the ring, bright and upright. The other sits inside it, fainter and mirror-flipped. The two paths differ in length and in how deep they dip into gravity, so the light takes different times. Here, with the core 0.6 Einstein radii off-axis, the inner image arrives 11.9 days after the outer one.
In real lenses the two images of the Twin Quasar differ by 417 days, and supernova Refsdal, split by a galaxy cluster, reappeared in December 2015, 376 days after its first images, as predicted. Inside the Milky Way a star lensing another star does the same with images a milliarcsecond apart. Telescopes see only a brightening that lasts weeks. This microlensing has revealed almost 300 planets, one of them only about 5.5 Earth masses.
μ = (u² + 2) / (u √(u² + 4)) total magnification · u = offset in Einstein radii Δt = (1 + zL) · 4GM/c³ · F(u) time delay between the images F(u) = u √(u² + 4) / 2 + ln[ (√(u² + 4) + u) / (√(u² + 4) − u) ]What does a black hole really look like?
Near a black hole, gentle bending turns extreme. At 1.5 Schwarzschild radii light can orbit, unstably: the photon sphere. Any ray aimed within 2.6 rs of the centre (exactly √27/2) spirals in, so a distant observer sees a black disk 2.6 times wider than the horizon: the shadow. In Up close, every pixel of the picture follows a real ray of light backward from the camera, along the exact path Einstein's equations give around a non-rotating black hole: past it, around it, or into it.
Gas falling toward a black hole settles into a thin disk and spirals in. At its inner edge, three Schwarzschild radii out, the gas orbits at half the speed of light; a little farther out it is hottest: about 25 000 K for a disk around M87*, shining at a tenth of the Eddington limit (the brightness at which the push of its own light balances gravity). Up close always shows a hole as heavy as M87*, 6.5 × 10⁹ solar masses. Gravity bends the light of the disk's far side up over the black hole, so you see the top of the disk behind it like a hat, and it shows the disk's underside as a thin ring hugging the shadow. Motion changes brightness: where the gas rushes toward you its light is squeezed to higher frequency and beamed forward; where it recedes, its light is stretched and dimmed.
Jean-Pierre Luminet drew this picture by hand in 1979, dot by dot, from the output of an IBM 7040. For the film Interstellar the effects team kept the bending but left out the lopsided brightness. In 2019 the Event Horizon Telescope imaged the glowing ring around M87*: 42 ± 3 microarcseconds across, where relativity predicts a shadow edge of 39.7 µas (EHT fitted that mass to the ring, so this agreement is partly circular). In 2022 it imaged our own Sgr A*: 51.8 ± 2.3 µas, against 53.3 µas predicted from its mass, weighed independently by the stars that orbit it.
sin αsh = (bc / r) · √(1 − rs/r) shadow radius seen from r · bc = √27/2 rs Tseen = g · Temitted Doppler + gravitational shift · brightness × g⁴ over all wavelengthsThe numbers
| Quantity | Meaning | Value |
|---|---|---|
| Light bending at the Sun's edge | Newtonian estimate 0.875″; 1919: 1.98 ± 0.12″ (Sobral), 1.60 ± 0.31″ (Príncipe) | 1.75″ |
| Einstein radius (default) | 3 × 10¹⁰ M☉, halfway (comoving) to a galaxy at z = 1 | 0.32″ |
| Einstein radius at the lens | 640 000 Schwarzschild radii: why the hole itself is invisible from Earth | 1.85kpc |
| Time delay at u = 0.6 | outer image first; zero for a perfect ring | 11.9days |
| Photon sphere | light can orbit here, unstably | 1.5rₛ |
| Shadow radius, seen from far | √27/2 rs: any ray aimed inside is captured | 2.598rₛ |
| Inner edge of the disk | the innermost stable orbit, where the gas moves at 0.5 c | 3rₛ |
| Hottest disk gas | M87* mass, fed at 10 % of the Eddington limit (Sgr A* mass: 154 000 K) | 24 700K |
| M87* ring (EHT 2019) | shadow edge for 6.5 × 10⁹ M☉ at 16.8 Mpc: 39.7 µas (mass fitted to the ring) | 42 ± 3µas |
| Sgr A* ring (EHT 2022) | shadow edge for 4.30 × 10⁶ M☉ (GRAVITY) at 8 277 pc: 53.3 µas | 51.8 ± 2.3µas |
| SN Refsdal delay | a supernova seen again, on schedule | 376days |
What's simplified
- A lone point mass. A real supermassive black hole sits inside a galaxy whose stars and dark matter do most of the lensing (the Abell 1201 black hole was found as a small extra distortion of such a lens). Above 5 × 10¹⁰ M☉ the caption says so.
- Thin lens, weak field. Side and From Earth use the thin-lens, weak-field approximation, which is excellent 640 000 rs from the hole. Up close integrates exact Schwarzschild light paths.
- Stretched angles, a giant Earth. Side view: not to scale, with angles stretched by 2 × 10⁴ to 1.7 × 10⁶ depending on the mass (7.7 × 10⁴ at the default, 1.5 times more on phones), Earth and its telescope drawn enormous, and light pulses sped up about 6 × 10¹⁶ times. Where the drawn angles grow large the straight-line drawing departs from the exact stretch, and the tag says ≈. Distances along the axis are comoving, and the black hole stays between 0.12 and 0.88 of the way so it never sits on Earth or on the galaxy. When the mass drops, Side keeps the hole within 3 Einstein radii of the line of sight so both paths still show; From Earth leaves it where it is.
- One procedural galaxy. The galaxy is procedural and placed at z = 1. The magnification readout treats its core as a point of light, like a quasar: the core is drawn 50 pc wide, but a real quasar's light comes from a region far smaller, which is why it can brighten more than 1000 times at perfect alignment. Foreground stars are not lensed, because they are in front of the lens.
- No spin. Up close, the hole does not rotate. A spinning hole would squash the shadow slightly and pull the disk's inner edge inward; real holes probably spin.
- A textbook disk. Thin, opaque and steady (Novikov–Thorne), fed like a quasar at 10 % of the Eddington limit; today's Sgr A* and M87* are fed far less. Its clumps and the hot spot are an illustrative pattern moving at the true orbital speeds, sped up (1 s on screen = 10 GM/c³). The disk turns so that its right side comes toward you. It stops at 30 GM/c² with a soft edge; gas plunging inside the innermost stable orbit is not drawn; on phones the disk's pattern ignores the light-travel delay across the image.
- Boosted stars, a hovering camera. A camera exposed for the disk would not see the stars at all. The galaxy behind the hole is drawn about 10 000 times larger than it would really look, and the Milky Way band is illustrative. The camera holds still at its distance, which would take an enormous rocket.
Myths
Sources
- Narayan & Bartelmann, Lectures on Gravitational Lensing — arXiv
- C. M. Will (2015), The 1919 measurement of the deflection of light — arXiv
- Einstein ring — Wikipedia
- June 9, 1988: first image of an Einstein ring (MG1131+0456) — Astronomy
- Kelly et al. (2023), SN Refsdal time delay — arXiv
- Nightingale et al. (2023), a black hole in Abell 1201 found by strong lensing — MNRAS
- Beaulieu et al. (2006), a 5.5 Earth-mass planet found by microlensing — arXiv
- Planck 2018 results VI, cosmological parameters — arXiv
- James, von Tunzelmann, Franklin & Thorne (2015), Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar — arXiv
- Luminet (2019), An illustrated history of black hole imaging — arXiv
- Gralla, Holz & Wald (2019), Black hole shadows, photon rings, and lensing rings — arXiv
- Iyer & Petters (2007), Light's bending angle due to black holes — arXiv
- Abramowicz & Fragile (2013), Foundations of black hole accretion disk theory — Living Reviews / arXiv
- GRAVITY Collaboration (2022), Mass distribution in the Galactic Centre — arXiv
- EHT Collaboration (2019), First M87 Event Horizon Telescope Results I — arXiv
- EHT Collaboration, First Sagittarius A* Results I — arXiv
- Perlick & Tsupko, black hole shadows for observers at finite distance — arXiv
- ESO / EHT (2022), first image of Sgr A*, the black hole at the centre of the Milky Way — ESO
- EHT Collaboration, First Sagittarius A* Results V: how fast Sgr A* is fed — arXiv
- Twin Quasar, the first lensed quasar, 417 ± 3 day delay — Wikipedia
- NASA Exoplanet Archive, planets discovered by microlensing — NASA
