Mathematicians discover an infinite number of possible black hole shapes.


It looks like the cosmos To have a preference for round objects. Planets and stars tend to be spherical because gravity pulls clouds of gas and dust toward the center of mass. The same is true for black holes – or more precisely, the event horizon of black holes – according to theory, the universe should be spherical in three dimensions and one in time.

But do the same constraints apply if our universe has a higher dimension, as it is sometimes postulated—with effects that we cannot see but are still palpable? Could there be other forms of black holes in those settings?

The answer to the latter question, mathematics tells us, is yes. Over the past two decades, researchers have discovered occasional exceptions to the law that constrains black holes to a spherical shape.

Now a new paper goes even further, showing with stunning mathematical proof that an infinite number of shapes of numbers five and above can be achieved. The paper shows that Albert Einstein’s equations of general relativity produce a large number of peculiar-looking, supermassive black holes.

The new work is only theoretical. It does not tell us that such black holes exist in nature. But Marcus Khoury, a geologist at Stony Brook University, said such strangely shaped black holes — likely the microscopic effects of particle collisions — “reveal that our universe is massive.” Co-author of the new work with Jordan Raynon, a recent Stony Brook math Ph.D. “So we’re just waiting to see if our experiment can detect anything.”

Black Hole Donuts

As with many stories about black holes, it begins with Stephen Hawking—specifically, with his 1972 assertion that the surface of a black hole must, at some point in time, be a two-dimensional sphere. (While a black hole is a three-dimensional object, its surface is only two-dimensional.)

Little thought was given to extending Hawking’s theory until the 1980s and ’90s, when enthusiasm for string theory—an idea that required the existence of perhaps 10 or 11 dimensions—came. Physicists and mathematicians began to think seriously about what these extra dimensions might mean for black hole topology.

Black holes are the most perplexing predictions of Einstein’s equations—10 connected nonlinear differential equations that are surprisingly difficult to deal with. In general, they are clearly solvable only in highly symmetric, and therefore simple, situations.

In the year In 2002, three decades after Hawking’s result, physicists Roberto Imparan and Harvey Real – now at the University of Barcelona and Cambridge, respectively – found a highly symmetric black hole solution to Einstein’s equations in five dimensions (plus four spaces). at once). Emparan and Riel call this object the “black ring”—a three-dimensional outline of the donut’s overall appearance.

A three-dimensional figure is difficult to draw in a five-dimensional space, so let’s imagine a simple circle instead. For each point on that circle, we can substitute a two-dimensional sphere. The result of this combination of circle and sphere is a three-dimensional object that can be thought of as a solid, dense doughnut.

In principle, donut-like black holes can form if they spin at the right speed. “If they’re spinning too fast, they’ll fall apart, and if they’re not spinning fast enough, they’ll go back into a ball,” Rainon said. “Emparan and Reall have found a sweet spot: their ring spins fast enough to stay like a donut.”


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