What shape is a black hole? Many of us think of black holes as funnels due to depictions of them throughout history. However, if we look to definitively answer the question, we must consider an infinite number of shapes that the human mind cannot even picture. According to Stephen Hawking, a black hole’s event horizon does not have to be a sphere, but it does have to be topologically spherical. This means that any shape can be turned into a sphere without changing the number of holes in it. The Event Horizon Telescope has even seen donut-looking shapes in the real world, although these are created by the light surrounding the black hole. If a black hole is ever observed to be donut-shaped, it could mean that a fourth spatial dimension has been hiding under our noses all this time. Despite how delicious a black hole donut may seem to ponder, or how good it may look on a mug, there may be another topology out there. This topology is so difficult to picture that scientists choose not to and instead 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. What is a lens space? It is sometimes described as a folded-up sphere and is the next simplest topology after a sphere. To understand the general concept, we can visualize it with a hair tie. Lens spaces use rotations to tie two or more points on the shape together. We can make these points line up on top of one another with one twist of the hair tie. In a real lens space, these points would occupy the same space and the circle would be collapsed to half its original size. We can make the circle one third of its original size with two twists. 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. There are an infinite number of lens spaces one can create and they can be created in any number of dimensions greater than our current count. To support a black lens structure like this, researchers had to introduce an exotic kind of matter that isn’t accounted for in our current models of reality. We have yet to observe any evidence of non-spherical black holes and we don’t know how an extra dimension would interact with the ones we know and love. Therefore, we can’t really say what a black ring or black lens would look like to us.

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