Black holes rotate in space. As matter falls into them, they start to spin faster; if that matter has charge, they also become electrically charged. In principle, a black hole can reach a point where it has as much charge or spin as it possibly can, given its mass. Such a black hole is called “extremal” — the extreme of the extremes. These black holes have some bizarre properties. In particular, the so-called surface gravity at the boundary, or event horizon, of such a black hole is zero. “It is a black hole whose surface doesn’t attract things anymore,” said Carsten Gundlach, a mathematical physicist at the University of Southampton. But if you were to nudge a particle slightly toward the black hole’s center, it would be unable to escape.

In 1973, the prominent physicists Stephen Hawking, James Bardeen and Brandon Carter asserted that extremal black holes can’t exist in the real world — that there is simply no plausible way that they can form. Nevertheless, for the past 50 years, extremal black holes have served as useful models in theoretical physics. “They have nice symmetries that make it easier to calculate things,” said Gaurav Khanna of the University of Rhode Island, and this allows physicists to test theories about the mysterious relationship between quantum mechanics and gravity. Now two mathematicians have proved Hawking and his colleagues wrong. The new work — contained in a pair of recent papers by Christoph Kehle of the Massachusetts Institute of Technology and Ryan Unger of Stanford University and the University of California, Berkeley — demonstrates that there is nothing in our known laws of physics to prevent the formation of an extremal black hole.

Their mathematical proof is “beautiful, technically innovative and physically surprising,” said Mihalis Dafermos, a mathematician at Princeton University (and Kehle’s and Unger’s doctoral adviser). It hints at a potentially richer and more varied universe in which “extremal black holes could be out there astrophysically,” he added. That doesn’t mean they are. “Just because a mathematical solution exists that has nice properties doesn’t necessarily mean that nature will make use of it,” Khanna said. “But if we somehow find one, that would really [make] us think about what we are missing.” Such a discovery, he noted, has the potential to raise “some pretty radical kinds of questions.” Before Kehle and Unger’s proof, there was good reason to believe that extremal black holes couldn’t exist.

Hawking, Bardeen, and Carter believed there was no way an extremal black hole could form, according to the article, and “in 1986, a physicist named Werner Israel seemed to put the issue to rest.”

But the two mathematicians, studying the formation of electrically charged black holes, stumbled into a counterexample — and along the way “also constructed two other solutions to Einstein’s equations of general relativity that involved different ways of adding charge to a black hole.

Having disproved Bardeen, Carter and Hawking’s hypothesis in three different contexts, the work should leave no doubt, Unger said… “This is a beautiful example of math giving back to physics,” said Elena Giorgi, a mathematician at Columbia University….

In the meantime, a better understanding of extremal black holes can provide further insights into near-extremal black holes, which are thought to be plentiful in the universe. “Einstein didn’t think that black holes could be real [because] they’re just too weird,” Khanna said. “But now we know the universe is teeming with black holes.”

For similar reasons, he added, “we shouldn’t give up on extremal black holes. I just don’t want to put limits on nature’s creativity.”

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