Now two mathematicians have proved Hawking and his colleagues wrong. The new work — contained in two recent papers by Christoph Kehle of the Massachusetts Institute of Technology and Ryan Unger of Stanford University and the University of California, Berkeley — proves that there is nothing in our known laws of physics to prevent an extreme black hole from forming.
Their mathematical proof is “beautiful, technically innovative, and physically surprising,” said Princeton University mathematician Mihalis Dafermos (and Kehle and Unger’s PhD advisor). It points to a potentially richer and more diverse universe in which “there could be astrophysically extreme black holes,” he added.
That doesn’t mean they are. “Just because there’s a mathematical solution that has nice properties doesn’t necessarily mean that nature will use it,” Khanna said. “But if we found one, it really would be. [make] we’re thinking about what we’re missing.” Such a discovery, he noted, has the potential to raise “some pretty radical kinds of questions.”
The law of impossibility
Before Kehle and Unger’s proof, there was good reason to believe that extreme black holes could not exist.
In 1973, Bardeen, Carter, and Hawking presented four laws for the behavior of black holes. They recalled the four long-established laws of thermodynamics—a set of sacred principles that say, 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 their first three laws of black hole thermodynamics: the zeroth, first, and second laws. By extension, they assumed that the third law (as well as its standard thermodynamic counterpart) would also be true, although they were not yet able to prove it.
This law stated that the surface gravity of a black hole could not drop to zero in finite time—in other words, that there was no way to create an extreme black hole. To support their claim, the trio argued that any process that would allow a black hole’s charge or spin to reach an extreme limit could also potentially lead to the event horizon disappearing entirely. It is widely believed that black holes without an event horizon, called bare singularities, cannot exist. Furthermore, since the temperature of a black hole 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 that black holes must do.
In 1986, physicist Werner Israel appeared to settle the matter when he published a proof of the third law. Let’s say you want to create an extreme black hole from an ordinary one. You can try to do this by speeding up the rotation or adding more charged particles. The Israeli evidence seems to demonstrate that this cannot make the black hole’s surface gravity drop to zero at finite time.
As Kehle and Unger eventually discovered, Israel’s argument concealed a flaw.
Death of the Third Law
Kehle and Unger weren’t trying to find extreme black holes. They came across them by accident.
They studied the formation of electrically charged black holes. “We realized we could do this” — create a black hole — “for all charge-to-mass ratios,” Kehle said. This included the case where the charge is as high as possible, which is the sign of an extreme black hole.
Dafermos recognized that his former students had uncovered a counterexample to Bardeen, Carter, and Hawking’s third law: They had shown that they could indeed turn a typical black hole into an extreme one in a finite amount of time.
Kehle and Unger started with a non-rotating, uncharged 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 give it a charge.
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