Now, two mathematicians have proven Hawking and his colleagues wrong. The new work, included in two recent papers by Christoph Kehle of MIT and Ryan Unger of Stanford University and the University of California, Berkeley, shows that there is nothing in the laws of physics we know to prevent the formation of poles. Worth a black hole.
Mihalis Dafermos, a Princeton University mathematician who was Keller and Unger’s doctoral advisor, said their mathematical proof was “beautiful, technically innovative, and physically surprising.” He added that this hints at a potentially richer and more diverse universe in which “astrophysically extreme black holes may exist”.
But that doesn’t mean they are. “Just because there is a mathematical solution with good properties, it doesn’t necessarily mean that nature will exploit it,” Khanna said. “But if we somehow found one, that would really be the case. [make] We think about what we are missing. He noted that such a discovery could raise “some pretty radical questions.”
law of impossibility
Before Keller and Unger’s proof, there were good reasons to believe that extremal black holes could not exist.
In 1973, Bardeen, Carter, and Hawking proposed four laws about the behavior of black holes. They are similar to the time-honored Four Laws of Thermodynamics—a set of sacred principles that state, for example, that the universe becomes more disordered over time and that energy cannot be created or destroyed.
In their paper, the physicists demonstrated the first three laws of black hole thermodynamics: the zeroth law, the first law, and the second law. By extension, they assume that the third law (like its standard thermodynamic counterpart) is also true, although they have not yet been able to prove this.
This law stipulates that the surface gravity of a black hole cannot drop to zero in a limited time. In other words, there is no way to create an extremal black hole. In support of their claim, the trio argued that any process that allows a black hole’s charge or spin to reach extreme limits could also cause its event horizon to disappear entirely. It is generally believed that a black hole without an event horizon (called a naked singularity) 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 also has 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 published a proof of the third law that seemed to resolve the problem. Suppose you want to create an extremal black hole from an ordinary black hole. You can try to do this by making it spin faster or adding more charged particles. Israel’s demonstration seemed to show that doing so would not force the black hole’s surface gravity to drop to zero for a limited time.
As Keller and Unger eventually discovered, Israel’s argument masked a flaw.
Death of the Third Law
Keller and Unger did not set out to find extremal black holes. They stumbled upon it completely by accident.
They are studying the formation of electrically charged black holes. “We realized we could do it” — make a black hole — “for all charge-to-mass ratios,” Keller said. These include situations where the charge is as high as possible, a hallmark of extreme black holes.
Daphermus realized 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 extreme black hole in a limited amount of time.
Starting with a non-rotating and uncharged black hole, Keller and Unger simulated 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 blasted the black hole with pulses from the field, adding an electric charge to it.
