Now two mathematicians have proven Hawking and his colleagues wrong. The fresh work — contained in Couple Latest Articles By Christopher Kehle Massachusetts Institute of Technology and Ryan Unger from Stanford University and the University of California at Berkeley — proves that there is nothing in the known laws of physics that prevents extreme black holes from forming.
Their mathematical proof is “beautiful, technically innovative and physically surprising,” he said. Michael Dafermosmathematician at Princeton University (and Kehle and Unger’s doctoral advisor). This suggests a potentially richer and more diverse universe in which “extreme black holes could exist astrophysically,” he added.
That doesn’t mean it is. “Just because there’s a mathematical solution with nice properties doesn’t necessarily mean nature will use it,” Khanna said. “But if we somehow find it, that’s really [make] think about what we’re losing.” 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 was reason to believe that extreme black holes could not exist.
In 1973, Bardeen, Carter, and Hawking proposed four laws of black hole behavior. They were similar to the long-established four laws of thermodynamics—a set of sacred rules that say, for example, that the universe becomes more disorderly over time and that energy cannot be created or destroyed.
In their work, physicists proved their first three laws of black hole thermodynamics: the zeroth, first, and second. They therefore assumed that the third law (like its standard thermodynamic counterpart) would also be true, although they were not yet able to prove it.
This law stated that a black hole’s surface gravity 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 allowed a black hole’s charge or spin to reach an extreme limit could also potentially cause its event horizon to disappear altogether. It is widely believed that black holes without an event horizon, called naked singularities, cannot exist. Moreover, 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 that Hawking later proposed that black holes must do.
In 1986, a physicist named Werner Israel seemed to have solved this problem when proof has been published of the Third Law. Say you wanted to create an extreme black hole from an ordinary one. You could try to do this by speeding up its spin or by adding more charged particles. Israel’s proof seemed to show that such an action could not force the surface gravity of a black hole to drop to zero in a finite time.
As Kehle and Unger eventually discovered, Israel’s argument had a flaw.
Death of the Third Law
Kehle and Unger didn’t set out to find extreme black holes. They stumbled upon them entirely 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 hallmark of an extreme black hole.
Dafermos noted that his former students had discovered a counterexample to Bardeen, Carter, and Hawking’s third law: they had shown that they could indeed turn a typical black hole into an extremal one within a finite time interval.
Kehle and Unger started with a black hole that doesn’t spin and has no charge, and modeled what would happen if they put it in a simplified environment called a scalar field, which assumes a background of uniformly charged particles. Then they hit the black hole with pulses from the field to give it charge.