An exploration · general relativity

Falling into a black hole

A trip from 84.9 AU out to the center of Sagittarius A*. Every frame is computed by tracing light through the curved spacetime of a black hole, so the view is what general relativity predicts a traveler would see, from the bent starlight to the sky inside the horizon.

Center of the Milky Way, 26,000 light-years away.

Sagittarius A* is starving. It shines at a few billionths of the Eddington limit, the most a black hole can emit before its own light pushes infalling gas away. Instead of a bright disk it has a faint, hot, puffy flow. Several times a day it flares, and in 2018 the GRAVITY instrument watched flares circle it at about 30% of the speed of light, once every 45 minutes or so, just outside the ISCO. The bright spot circling the hole here is one of those flares.

Scroll to fall · drag to look around ·

01500 rₛ

Far away, gravity is ordinary

Distances on this trip are measured in Schwarzschild radii, r_s = 2GM/c², the radius of the event horizon. For Sagittarius A* that is 12.7 million km, 18.3 times the radius of the Sun. In these units the geometry of every non-spinning black hole is identical: the same shadow, the same bent light, the same horizon. What changes from one to the next is the scale, the tides, and what surrounds it. Switch black holes at the top right and the gas, jets, and neighbors change with it.

Out here Newton's gravity is accurate to about one part in a thousand. A clock hovering at 500 r_s runs slow by a factor √(1 − r_s/r) compared with one far away, losing 86 seconds a day. You are not hovering. You were dropped from rest far away, and you will fall straight in. From here to the center takes 3.65 days on your own clock.

How the picture is made

For each pixel, the program follows a ray of light backward from your eye through curved space until it hits the glowing disk of gas, falls into the horizon, or escapes to the stars. The paths come from the equation of motion for light around a non-spinning black hole. Your own speed also bends and shifts the light you catch, the same way starlight looks different from a fast spaceship, and that is included too.

0260 rₛ

Light bends

Light follows the straightest possible paths through spacetime, and near mass those paths curve. Far from the hole, a ray passing at distance b is bent by about 2r_s/b radians. For the Sun that comes to 1.75 arcseconds at its edge, which Eddington's expedition measured during the 1919 eclipse.

Close in, the bending is large. Stars behind the hole are smeared into arcs around the black shadow, and each one appears twice, once on each side. A star exactly behind the hole would become a full circle, an Einstein ring.

Light passing a black hole, seen from above

impact parameter b3.400 r_s · 0.289 AU

bent by: 68.8°
Einstein's weak-field estimate: 33.7°

Each line is a light ray entering from the left, offset from the center by its impact parameter b. Rays with b below 2.598 r_s fall in. That number sets the size of the black shadow you see: about 2.6 times the horizon radius, not 1. Computed by integrating the Schwarzschild orbit equation for light.

0318 rₛ

The disk that isn't where it looks

Gas orbiting the hole settles into a thin disk and heats up until it glows. You are seeing it almost edge-on, yet it seems to wrap over the top and under the bottom of the shadow. The arc over the top is the far side of the disk: its light climbs over the hole to reach you. The thin ring under the shadow is the underside of that same far side, bent around the bottom. Jean-Pierre Luminet computed this image in 1979 on an IBM 7040 and drew the result by hand.

The left side is brighter because it is coming toward you. Gas at the inner edge orbits at 0.5c, so light from the approaching side is blueshifted and concentrated in your direction, and light from the receding side is redshifted and spread out. Light climbing out of the hole's gravity also loses energy, which dims the inner edge.

What is honest here and what isn't

The shapes and the frequency shifts are computed. The gas colors are visible-light stand-ins: the disk here peaks near 3800 K, while the real gas is millions of degrees and shines in ultraviolet and X-rays (or, around Sagittarius A*, glows faintly in radio). Brightness is relative: the camera exposure changes with each black hole, the way a real camera would. The jets, hot gas, and flares are simple models placed in the curved spacetime, so their light is lensed and shifted like the disk's.

043 rₛ · ISCO

The last stable orbit

In Newton's gravity a circular orbit exists at every radius. In general relativity, orbits inside 3 r_s are unstable: nudge the gas inward and it spirals in within a few orbits. That radius is the innermost stable circular orbit, the ISCO, and it is why the disk has an inner edge.

By the time gas reaches the ISCO it has radiated 5.7% of its rest-mass energy as heat and light. Hydrogen fusion in the Sun releases 0.7%. That eightfold difference is why a quasar, a black hole swallowing gas, can outshine every star in its galaxy.

Hovering here would take 39,700 g of rocket thrust. You are falling, so you feel nothing at all. Free fall is weightlessness, even here.

What the ISCO sounds like

Space carries no sound, so this is a sonification. Gas at the ISCO of Sagittarius A* completes an orbit every 32.6 min, a frequency of 5.1×10⁻⁴ Hz. The tone you hear is that frequency raised 18 octaves. Its pitch swings up and down because the gas alternately approaches and recedes, and the tone is shifted by the same factor as the gas's light, between 0.50 and 1.19. The roar follows how fiercely the hole is feeding, the high chord follows the starlight overhead (listen to it drop after the horizon), and a rumble grows with the tides.

051.5 rₛ · photon sphere

Where light orbits

At 1.5 r_s, light moving sideways travels in a circle. The orbit is unstable, so no light stays, but rays that pass close to this radius loop around the hole once, twice, or more before escaping. They pile up into a thin bright line at the edge of the shadow, the photon ring, made of nested images of the whole sky.

For this stop the view has switched to hovering, with rockets pushing 278,000 g. You are looking sideways, along the photon sphere, with the hole to your left. The shadow covers exactly half of the sky: every ray aimed even slightly toward the hole falls in, and every ray aimed away escapes.

Switch to falling and the shadow shrinks. You would be passing hovering observers at 0.816c, and that speed shifts the apparent direction of incoming light toward your direction of motion, the same aberration that crowds stars ahead of a fast ship.

061.12 rₛ

Your clock and theirs

Imagine someone far away keeping track of your fall. By their accounting, your clock runs at (1 − r_s/r) of theirs: here, 0.11. Light you beam home is stretched by 1/(1 − √(r_s/r)), a factor of 18.2 at this radius.

As you near the horizon, those factors run to infinity. Your friend sees your signals redden, slow, and fade, and your image dims away within a few multiples of r_s/c (42.4 s for Sagittarius A*). They never see you cross. On your own clock, nothing slows down, and you cross a few moments later.

Your clock and a far-away clock during the same fall

your clock far-away clock

Both curves describe one fall from 6 r_s. The amber curve uses your wristwatch: you reach the horizon after 6.45 min and the center 28.2 s later. The blue curve uses the time coordinate of someone far away. In that time you approach the horizon forever and never cross it. Time on the axis is for Sagittarius A*.

071 rₛ · event horizon

Nothing happens at the horizon

You crossed it. There was no wall and no flash. The horizon is not made of anything. It is the boundary of the region from which light cannot get back out, and a traveler can only find out it was passed by doing the math afterward. Across your body, the tidal stretch here is 0.11 milli-g.

The black region is still below you and you never reach it: it is the part of your sky from which no light can arrive. The river picture below gives one way to see why light cannot leave.

Space falling inward · click to emit light

Hover to read the flow speed.

In Painlevé–Gullstrand coordinates, which use the clocks of observers dropped from far away, space behaves like a river flowing inward at v = c·√(r_s/r). Light always moves at c relative to the river. Outside the horizon the river is slower than light, so an outward pulse (amber) creeps away. At the horizon the river reaches c and the pulse stands still. Inside, even light aimed outward is carried to the center.

08inside

The center is in your future

Inside the horizon, the radius r stops behaving like a direction in space and behaves like time. Every possible path, including a light ray aimed outward, moves toward smaller r, the way every path in ordinary life moves toward later times. The singularity is not a place ahead of you that you could steer around. It is a moment, and it arrives for everyone.

Falling from rest far away, the trip from horizon to center takes (2/3) r_s/c, which for Sagittarius A* is 28.2 s. No path takes longer than (π/2) r_s/c, or 66.5 s. A well-timed rocket burn can stretch your remaining time toward that limit, but burning too long cuts it short again (Lewis and Kwan, 2007).

You are looking back up, the way you came. The universe outside is still there: light from outside keeps falling in after you. Straight overhead it reaches you with its frequency multiplied by 0.4, so the stars there look redder and dimmer. Around the edge of the dark region it is shifted toward blue.

09tides

Spaghettification

Gravity pulls your feet harder than your head. In free fall you do not feel gravity itself, but you do feel that difference, the tidal stretch, and it grows as 1/r³.

For Sagittarius A*, it reaches 100 g across your body, far beyond what anyone survives, at 0.0104 r_s, 132,528 km from the center. You would have 30.1 ms left. For almost the whole fall you would feel nothing.

Head-to-toe stretch on a 2 m body, by distance

Sagittarius A*M87*TON 618Cygnus X-1

Tidal stretch is 2GML/r³. At a fixed fraction of the horizon size it falls as 1/M², so bigger black holes are gentler at their horizons. A person falling into Cygnus X-1 is pulled apart about 2,193 km before reaching the horizon. Falling into Sagittarius A*, you cross the horizon without noticing.

10r → 0

Where the theory stops

General relativity predicts that tidal forces and density become infinite at r = 0, after a finite time. Most physicists read that as the theory reaching the edge of where it applies, not as a description of what happens. Describing it needs a quantum theory of gravity, and nobody has a tested one. The calculation, and the trip, stops here.

More explorations

Notes

What this simulation simplifies

The black hole does not spin. Real ones almost certainly do, and spin flattens one side of the shadow, drags the disk's inner edge inward, and changes the interior: a spinning black hole has a second, inner horizon. The interior shown here is that of an eternal, non-spinning hole.

The disk is thin, opaque, and colored at a temperature chosen for visibility. There are no jets, no magnetic fields, no hot corona. Frequency shifts are exact for blackbody light: a blackbody at temperature T seen with frequency factor g is a blackbody at gT. The two colored nebulae emit single spectral lines, hydrogen at 656 nm and oxygen at 501 nm, so shifts move them through the spectrum. Brightness passes through an exposure curve, like a camera.

You fall straight in from rest far away. The hovering view uses an observer held still by rockets. Light paths are integrated numerically per pixel with a fourth-order Runge–Kutta method, from the orbit equation u″ + u = (3/2) r_s u² for u = 1/r.

Sources and further reading