Mathematicians Find an Infinity of Possible Black Hole Shapes

can see the universe Prefer round things. Planets and stars tend to be spherical because gravity pulls clouds of gas and dust toward their centers of mass. The same is true for black holes (more precisely, the event horizon of a black hole). According to theory, a black hole should be spherically shaped in the universe with three dimensions of space and one dimension of time.

But if our universe has higher dimensions, as is sometimes assumed, do the same restrictions apply? Are other black hole shapes possible in those settings?

The answer to the latter question is, as math tells us, yes. Over the past two decades, researchers have found occasional exceptions to the rule that restricts black holes to spherical shapes.

A new paper now goes further, proving exhaustively mathematically that an infinite number of shapes are possible in five dimensions and above. can generate a wide variety of exotic high-dimensional black holes.

The new work is purely theoretical. I don’t know if such black holes exist in nature. But if we somehow detect such oddly shaped black holes, perhaps as microscopic products of collisions in particle colliders, then “it automatically suggests that our universe is of higher dimensions.” ‘, said Jordan Raynone, a geometer at Stony Brook University and a recent PhD in mathematics from Stony Brook, who co-authored the new work. “So we just have to wait and see if our experiments can detect anything.”

black hole donut

Like so many stories about black holes, this one begins with Stephen Hawking. Specifically, it begins with his 1972 proof that the surface of a black hole must be a two-dimensional sphere at a given point in time. (A black hole is a three-dimensional object, but its surface has only two spatial dimensions.)

Until the 1980s and 1990s, extending Hawking’s theorem was largely unthinkable, but enthusiasm for string theory (an idea that presumably requires the existence of 10 or 11 dimensions) grew. Physicists and mathematicians then began to seriously consider what these extra dimensions meant for Black and his hole topology.

Black holes are some of the most complex predictions of Einstein’s equations (10 linked nonlinear differential equations) and are very difficult to deal with. In general, they can be explicitly resolved only in highly symmetric and simplified situations.

In 2002, 30 years after Dr. Hawking’s results, physicists Roberto Emparin and Harvey Leal (now at the Universities of Barcelona and Cambridge, respectively) discovered five dimensions (four times space and one time). Emparan and Reall called this object the “black ring”. This is a three-dimensional surface with the general outline of a donut.

It’s hard to draw a 3D surface in 5D space, so let’s imagine a normal circle. All points of that circle can be replaced by a 2D sphere. The result of this combination of circles and spheres is a three-dimensional object that can be thought of as a hard, lumpy donut.

In principle, such a donut-shaped black hole could form if it were spinning at the right speed. “If it spins too fast, it will fall apart, and if it spins too slowly, it will bounce back into a ball,” Raynone says. “Emparan and Reall found the sweet spot. Their ring was spinning fast enough to stay on as a donut.”

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