What shape is a black hole?

Did the classic funnel of death just come to mind? Or was it the dark sphere  surrounded by a glowing disk of matter and light, as depicted  in the movie Interstellar?

Sure, that computer-generated image is a great example of what a supermassive black hole and its accretion disk would look  like if we could get close enough. But if you’re looking to  definitively answer the question “What shape is a black hole?”, you’re going to have to think beyond  the three dimensions you’re used to and consider an infinite number of shapes the human mind can’t even picture. [INTRO] Many of us think of black  holes as funnels thanks to all the artists throughout  history trying to depict what they do to space and time around them. All that mass, compacted into such  a small volume, deforms spacetime.

But spacetime has more dimensions to it than we can depict on a textbook page. Everything has to get flattened out for the purposes of high school physics. A funnel represents the general idea  that spacetime gets more and more deformed the closer you get to a  black hole’s central singularity, where all the matter collects.

So the shape of the black hole in  these drawings isn’t the funnel, it’s a circle at a specific  part of the funnel’s throat. This circle represents the event horizon, the black hole’s famous point-of-no-return. Since we can’t perceive anything beyond it, it’s the closest thing we have to a physical edge or surface of the black hole.

When we talk about a black hole’s shape, we’re talking about the  shape of the event horizon. And if we un-flatten a circle from  its one-dimensional circumference, we get the two-dimensional surface area of a ball, which mathematicians call a sphere. So black holes are spherical,  just like Interstellar showed us.

I guess question answered. We can all go home now. Thanks to our patrons– Ah!

Not so fast. According to Stephen Hawking,  a guy famous for trying to figure out this extreme astrophysical phenomenon, a black hole’s event horizon  doesn’t have to be a sphere. It does, however, have to  be topologically spherical.

So, what’s a topological sphere? It’s any shape you can turn into a sphere without changing the number of holes in it. So for example, if I have a hollow ball  of clay and I drop it on the floor, It’ll get flattened out a little bit.

So not a sphere, but it’s  still a topological sphere. And so is any shape I can  make by squishing different bits here and there, like this heart. I mean, sure, nature probably isn’t going to make a vaguely heart-shaped black hole.

But the math shows that it’s perfectly normal, if not typical, for black holes to be ellipsoidal. The physics gets way wonkier  when you get up close, but it’s the same reason why the  Earth isn’t a perfect spherical ball. They’re both spinning, which  squishes the shape a little bit.

But with all due respect to Hawking, his conception of these  things might not be complete. His math is only valid for 3D space. And our universe might not have  just three spatial dimensions.

In 2002, two scientists  proved that if space is 4D, a black hole spinning at just  the right speed can uphold the known laws of physics while looking  like a higher dimensional donut. And okay, fine, they don’t call it a donut, they call the structure a black ring. And if we break out the clay again, you can see how a donut and a ball  have two different topologies.

I mean, I can’t turn this sphere into  a donut without tearing it a new one. Now, thanks to the Event Horizon Telescope, we have seen black hole donut-looking  shapes in the real world. But these are created by the  light surrounding the black hole.

The dark central blob is the  shadow cast by the event horizon. We’ve yet to observe a black  hole that is itself donut-shaped. But if we do, it could mean  a fourth spatial dimension has been hiding under our noses all this time.

Now as delicious as a black  hole donut may be to ponder, or as good as one might look  on a mug, DFTBA.com/SciShow, there’s another topology that  could be out there as well. A topology that’s so difficult to picture  that scientists simply choose not to. They just stick to the math of it all.

In 2006, researchers proposed that  in a universe with four spatial dimensions, a black hole’s event  horizon could be a lens space. But okay, now it sounds like  they’re just making things up. What the heck is a lens space?

Lens spaces are sometimes  described as folded-up spheres, and after spheres, they’re the  next simplest topology out there. To understand the general concept, we’re going to drop all the way down to 1D. Now it’s technically not one dimensional, but we can visualize what we’re  about to do with a hair tie.

Lens spaces use rotations to tie two or more points on the shape together. So we’re going to do the simplest version of that: a rotation that’s half the circle. 180 degrees. For the visual, we’ve marked  a few different sets of points that are 180 degrees apart, so exactly  on opposite sides of one another.

Technically there are an infinite  number of points on this circle, but I’ve only got so many  colors, so this will have to do. Now if I make exactly one twist in this hair tie, I can make these points line  up on top of one another. And ta da.

We’ve done it! In a real lens space, these would occupy the exact same point in space. The circle would be collapsed to  exactly half its original size.

But like everyone who’s hair tie  has gotten a bit stretched out and needs to start doing another  twist to keep their ponytail intact, we don’t have to stop there. So we’ll twist it once, and  twist it again, and there, you have a completely different lens space, third ties three points together and makes the circle one third its original size. And with a big enough hair tie, you could do basically any number of twists.

Meanwhile, in 4D space, the  event horizon of a black hole would be a three-dimensional lens space. The folding is even more complicated, but the fundamental idea of  rotations stays the same, and there are an infinite number  of lens spaces you can create. Back in 2022, black hole lens spaces  were proven as mathematically legit for not just 4D space, but 5D, 6D,  literally as many Ds as you might need.

In other words, there are an  infinite number of shapes a black hole can be, no matter how  many dimensions the universe has, so long as it’s more than our current count. Now, it’s worth mentioning that to  support a black lens structure like this, the researchers had to introduce  an exotic kind of matter that isn’t accounted for in  our current models of reality. So this is all incredibly hypothetical.

As of right now, we’ve yet to observe any evidence of non-spherical black holes. And because we don’t know how an  extra dimension would interact with the ones we know and love, we  can’t really say what a black ring or black lens would look like to us. But I am all for another blockbuster sci-fi movie to show us what could be possible.

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