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Now, two mathematicians have shown that Hawking and his colleagues were wrong. The new work, which is published in a couple of Recent Articles by Christoph Kehle from the Massachusetts Institute of Technology and Ryan Unger from Stanford University and the University of California, Berkeley, shows that there is nothing in our known laws of physics that prevents the formation of an extreme black hole.

His mathematical proof is “beautiful, technically innovative and physically surprising,” he said. Mihalis Dafermosmathematician at Princeton University (and Kehle and Unger’s PhD advisor). This suggests a potentially richer and more varied universe in which “astrophysically there could be extreme black holes,” he added.

That doesn’t mean they are. “Just because there is a mathematical solution with nice properties doesn’t necessarily mean that nature is going to make use of it,” Khanna said. “But if we somehow find one, that would really make us think about what we’re missing.” Such a discovery, he noted, has the potential to raise “some pretty radical questions.”

## The law of impossibility

Before Kehle and Unger’s proof, there were good reasons to believe that extreme black holes could not exist.

In 1973, Bardeen, Carter, and Hawking introduced four laws of black hole behavior that resembled the long-established four laws of thermodynamics: a set of sacrosanct principles stating, for example, that the universe becomes more disordered over time and that energy can neither be created nor destroyed.

In their paper, the physicists proved the first three laws of black hole thermodynamics: the zeroth, the first, and the second. By extension, they assumed that the third law (like its counterpart in standard thermodynamics) would also hold true, although they have not yet been able to prove it.

That law stated that a black hole’s surface gravity cannot decrease to zero in a finite time — in other words, that there is no way to create an extreme black hole. To support their claim, the trio argued that any process that allowed a black hole’s charge or spin to reach the extreme limit could also potentially cause its event horizon to disappear entirely. It is widely believed that black holes without an event horizon, called naked singularities, cannot exist. Furthermore, since a black hole’s temperature is known to be proportional to its surface gravity, a black hole without surface gravity would also have no temperature. Such a black hole would not emit thermal radiation, something Hawking later proposed black holes must do.

In 1986, a physicist named Werner Israel seemed to settle the matter when… posted a test of the third law. Let’s say you want to create an extreme black hole out of a normal one. You can try to do this by making it spin faster or by adding more charged particles. Israel’s test seemed to show that doing so couldn’t force the surface gravity of a black hole to drop to zero in a finite time.

As Kehle and Unger would eventually discover, Israel’s argument concealed a flaw.

## The death of the third law

Kehle and Unger did not set out to find extreme black holes. They stumbled upon them purely by chance.

They were studying the formation of electrically charged black holes. “We realized we could do it” — create a black hole — “for all charge-to-mass ratios,” Kehle said. That included the case where the charge is as high as possible, a hallmark of an extreme black hole.

Dafermos acknowledged that his former students had discovered a counterexample to Bardeen, Carter and Hawking’s third law: they had shown that they could indeed transform a typical black hole into an extreme one in a finite period of time.

Kehle and Unger started with a non-rotating, chargeless black hole and modeled what might happen if it were placed in a simplified environment called a scalar field, which assumes a background of uniformly charged particles. They then hit the black hole with pulses from the field to add charge to it.