Thread by @tobyordoxford

DISSECTING A BLACK HOLE
I’ve designed a new kind of diagram for understanding black holes — and made a beautiful poster to show it off.
The key idea is to show the many different layers of a black hole, each with their own unique properties.
Let's dive in!
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I call this a ‘record diagram’.
By slicing through all of these spheres, we see the black hole laid out like a record on a turntable, displaying all its different tracks — both the classic hits that may have blurred together in lower fidelity diagrams and some deep cuts.
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Distances near black holes are best measured in units of M — a key distance based on the black hole’s mass. For a black hole the mass of our sun, M = 1.5 km. For a mass of a million suns, M = 1.5 million km.
Most interesting things happen when you pass integer multiples of M.
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By far the most famous distance is the Event Horizon, at 2M. It is certainly the black hole’s greatest hit, but most people think everything interesting happens here and that the event horizon *is* the black hole.
In truth, things start getting crazy 3 times further out.
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6M is the closest anything can stably orbit the black hole. All orbits inside 6M are unstable — the tiniest deviation can greatly change the orbit or send the object into the singularity.
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Many black holes have 'accretion disks' — swirling rings of incandescent material torn off other stars. The brightest ones glow brighter than all 100 billion suns of the entire Milky Way combined. 6M is the inner edge of this disk.
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On its way down towards 6M, the matter releases a staggering 5.7% of its rest mass as raw energy, powering that incredible glow. Even nuclear fusion releases less than 1% of its fuel’s mass as energy.
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Once the material reaches 6M there are no more stable orbits so without any way of correcting the instabilities it is inevitably drawn into the singularity.
But a spacecraft that could measure its orbit and apply small amounts of thrust to correct it could orbit closer in…
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4M is the Marginally Bound Orbit.
An object that falls towards the black hole from very far away could actually fall right into an unstable circular orbit at 4M, having been accelerated to 71% of the speed of light in the process.
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For a spacecraft that can correct these instabilities this could be a perfect vantage point for a scientific mission to a black hole (a quiet one without a blazing accretion disk…).
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It would require no fuel to fall into the 4M orbit, a tiny amount to park in it, a little more to keep adjusting instabilities, then another tiny thrust to fly back out to a great distance, in a direction of your choosing.
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Regular stars don’t have orbits like this — it requires a lot of thrust to get into a close orbit around the sun, then a lot to get back out again. But for black holes, you can go back and forth between 4M and extremely far away for arbitrarily little energy.
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Within 4M orbits are ‘unbound’ — they are so unstable that tiny deviations can now also fling you out arbitrarily far from the black hole. Spacecraft that can do orbital adjustments could orbit closer in than 4M, but would need to use some energy to get there.
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Orbiting at 4M required a speed of 71% of c, but luckily you could get this from the acceleration of falling that far in. Closer orbits require higher speeds and thus a *lot* of extra energy. As you approach 3M, the required speed approaches 100% of the speed of light.
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So 3M is the distance at which only light is fast enough to orbit. The sphere at this radius is known as the ‘photon sphere’, as light could travel around it in circles. However the orbit is still unstable, so in practice it will eventually fly off to the distance or fall in.
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If light ever goes inside 3M, it will fall all the way to the singularity. 3M is the point of no return for light.
Unless, that is, it were to bounce off a mirror or other surface suspended between 2M and 3M…
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For yes, even though there are no *orbits* for matter or light within 3M, it is possible for a spacecraft to hover or fly there if using extreme amounts of thrust. And light that is directed *away* from the black hole can still escape.
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But even these approaches fail at 2M — the Event Horizon. That is the ultimate point of no return. Nothing can hover within a distance of 2M and even light shone straight up would not be fast enough to escape.
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Like the other spheres at 6M, 4M, and 3M, the event horizon is an imaginary in space. I say 'imaginary', because it isn’t like the surface of planet or billiard ball. It is more like a border between countries—it matters, but you can’t see it or easily tell if you go past it.
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Indeed for a supermassive black hole, the tidal forces are so weak at the event horizon that you could survive the forces there. Indeed they are so weak that you may not be able to notice the point when you cross 2M.
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Within 2M everything inexorably moves down towards the conjectured singularity at 0M, where all the black hole’s mass is located at a point of zero volume. No object and no information can escape.
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Hawking radiation is emitted from the event horizon, but it is a random pattern of particles carrying no information about what has happened inside.
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So as you can see, there are important thresholds at 6M, 4M, 3M, 2M, and 0M. This is all for a simple non-charged, non-rotating black hole. Rotating black holes also have thresholds at 1M and 9M.
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But there is one other key radius I want to mention. When you see an image of a black silhouette against the stars, what are you seeing?
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Most people think you are seeing the event horizon, which they think of as the black hole itself. But it is perhaps more accurate to say you are seeing the photon sphere, as that is the distance at which (absent a hovering mirror…) no incoming light will ever return.
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So is the radius of the black circle you see equal to 3M? No, it is actually equal to 5.19615… M. Even in its closed form of 3√3 M, this is an unusual radius. This sphere is called the *shadow* of the black hole.
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It is larger than the photon sphere because of how light is bent by the black hole. Light from behind the black hole that is up to 3√3M off axis gets bent towards the black hole as it approaches and eventually crosses the photon sphere and never leaves.
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Indeed light that is *exactly* 3√3 M off axis is bent around until it just grazes the photon sphere and could in theory park there in orbit at 3M, just like how material objects can fall into the orbit at 4M.
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Unlike the other layers at integer multiples of M, the shadow isn’t a boundary where something new happens inside the black hole. It is just how big the black hole appears from a long way away.
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As you come closer, the apparent black sphere strangely appears to shrink a little in absolute terms — as if its surface were pulling away from you.
By 3M it occupies half your view, as if you were on the surface of a black planet of radius 3M, with distorted stars above.
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Below 3M the starry field that occupied the top half of your view would shrink smaller and smaller as if you were descending a black well. These directions in which you can still see light are also the only directions in which any light you shine would escape.
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Finally, at the event horizon (2M), the circle of stars above you would shrink to a point and everything would be blackness.
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Which is a fitting end for our deep dive through the many layers of a black hole.
I hope you’ve enjoyed the ride, seeing beyond the event horizon to the many other interesting spheres that surround a black hole, each with their own properties.
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Here is the full black hole poster, showing all of this and more.
I’ve included download links for high resolution versions (high enough to print an epic poster), as well as a special zoomable image. Enjoy!
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tobyord.com/black-hole