# The Planck Dive

## Cordelia’s Tour

### The view from near, and inside, a black hole

If you have Java, you can generate the view from any position and angle with the black hole view applet. And if you’re interested in the physics behind these views, there’s a detailed account in the technical notes.

Below are views at various distances from a black hole. These are wide-angle shots, each about 127° across (the same apparent width as a 4-metre object just 1 metre away). Distances are given in the “Schwarzschild r” coordinate — the circumference of a circle centred on the hole, divided by 2 π — and in units of “M”, which is a scale determined by the mass of the hole. For Chandrasekhar, a twelve solar-mass hole, M = 17.6 km. The event horizon lies at r = 2 M.

All views are for the closest thing possible to a “stationary” observer. Outside the hole, they’re for an observer with a fixed Schwarzschild r coordinate. Inside the hole, it’s physically impossible to stay at the same r, so they’re for an observer with a fixed “Schwarzschild t” coordinate — a measure of time outside the hole, which becomes a measure of space inside. An observer who fell freely into the hole would see different blue shifts and aberration.

Note: Due to the limited palettes available, the red and blue shifts in these diagrams are highly stylised, and the secondary images of stars are shown as being brighter than they would be in reality. (Actual red and blue shifts are plotted below, and brightness effects are discussed at the end of the technical notes.)

Looking towards the hole Looking away from the hole
At a distance of 10 M
At a distance of 6 M
Four of the paths light rays from a single direction can follow Shrinking of sky opposite the hole: two rays from left and right appear to be arriving from a narrower angle.

The hole appears to be surrounded by a halo of stars. Gravitational lensing lets you see the stars directly behind the hole, but it doesn’t stop there; light that comes close to being captured can be bent through extremely large angles, even orbiting the hole completely one or more times before eventually escaping (above left.) So the halo consists of a series of concentric images of the entire sky, each made up of light that has orbited the hole one more time.

Looking in the opposite direction, as you approach the hole the stars appear increasingly crowded together, as incoming light rays are bent into more radial paths (above right.)

At a distance of 3 M

By 3 M, the hole and the sky each occupy precisely one hemisphere. This view looks sideways, straight into the starlight that spirals around the hole.

At 2.5 M, two images of the sky are clearly visible (and a narrow third image can just be made out). The dark band that seems to separate them is due to the fact that a small region of the sky directly behind the hole is spread out into a circle, making it seem particularly sparse. (If a star happened to lie in just the right direction, it would fill this band with light — creating the effect known as an “Einstein ring”.)

At a distance of 2.5 M
Blue shift factor vs. r/M (outside event horizon) At a distance of 2.1 M

By 2.1 M, the image of the sky is just 60° wide, and photon energies are blue-shifted by a factor of almost 5 — enough to make infrared radiation look blue, and to send all ordinary light into the ultraviolet.

Blue shift factor vs. r/M and angle from zenith (inside event horizon) At a distance of 1 M

From inside the hole, the sky spreads out again (though it never becomes wider than a hemisphere). The uniform blue shift gives way to a frequency shift that varies across the view: bluest at the edges, and (for r < 1 M) actually red-shifted at the centre.

This effect can be thought of either as a Doppler-shift “starbow” (due to your inevitable motion away from the event horizon) superimposed on the gravitational blue shift, or due to the fact that the space inside the hole is being squeezed in two directions while expanding in the third.

At a distance of 0.5 M

Reference: The equations on which these views are based were obtained by “the method of conserved quantities”, described in Sections 25.2 and 25.3 of Gravitation by Charles Misner, Kip Thorne and John Wheeler (see the technical notes for full details). My thanks to Geoffrey Landis, who pointed out problems with the brightness of secondary images in an earlier version of this page.

Greg Egan science fiction writer
The Planck Dive / Cordelia’s Tour / created Saturday, 25 October 1997 / revised Friday, 12 June 1998