Cosmos prefers round shapes, black holes can have infinite shapes in 5+ dimensions.
Black holes are incredibly mysterious objects predicted by Albert Einstein’s equations of general relativity. Historically, they have been thought of as spherical in shape, but recent research has shown that they can have a variety of shapes in higher dimensions. In 2002, Roberto Emparan and Harvey Reall discovered a doughnut-shaped black hole in five dimensions, and in 2006, Greg Galloway and Richard Schoen generalized Stephen Hawking’s theorem to describe all possible shapes that black holes could potentially assume in dimensions beyond four.
These shapes include spheres, doughnut-like black rings, and a broad class of objects called lens spaces. Lens spaces are a particular type of mathematical construction that has long been important in both geometry and topology. They are created by folding up a sphere in a very complicated way, and can be thought of as a solid, lumpy doughnut. In 2006, Greg Galloway and Richard Schoen generalized Stephen Hawking’s theorem to describe all possible shapes that black holes could potentially assume in dimensions beyond four.
In 2014, Hari Kunduri and James Lucietti proved the existence of a black hole of the L(2, 1) type in five dimensions. This black lens has a couple of important features, including that the curvature of space-time approaches zero as one moves toward infinity. This characteristic helps ensure that the results are physically relevant.
In their December 2022 paper, Khuri and Rainone generalized the Kunduri-Lucietti result about as far as one can go. They first proved the existence in five dimensions of black holes with lens topology L(p, q), for any value of p and q greater than or equal to 1. They also found that they could produce a black hole in the shape of any lens space, with any values of p and q.
The new work is purely theoretical, and does not tell us whether such black holes exist in nature. However, if we were to detect such oddly shaped black holes, it would automatically show that our universe is higher-dimensional. It is now a matter of waiting to see if our experiments can detect any. This research opens up a vast new realm of possible black hole shapes, and further research into this area could help us gain a better understanding of the universe and its higher dimensions.
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