The result doesn’t yet extend to Kerr black holes that rotate quickly with respect to their mass, which are also known to exist in the universe. “It’s a long paper, so it’s going to take some time,” Giorgi says. The work is currently undergoing peer review. The technique entails assuming the opposite of the statement to be proved, then discovering an inconsistency. In a nearly 1,000-page paper, Giorgi and colleagues used a type of “proof by contradiction” to show that Kerr black holes that rotate slowly (meaning they have a small angular momentum relative to their mass) are mathematically stable. Kerr’s solution helped establish the existence of black holes. “Physicists really had believed for decades that the black hole region was an artifact of symmetry that was appearing in the mathematical construction of this object but not in the real world,” Giorgi said in the talk. Rotating black holes were much more realistic astrophysical objects than the non-spinning black holes that Karl Schwarzschild had solved the equations for. This was a “game changer for black holes,” Giorgi noted in a public lecture given at the virtual 2022 International Congress of Mathematicians. Just a couple of years earlier, in 1963, New Zealand mathematician Roy Kerr found a solution to Einstein’s equation for a rotating black hole. In a landmark paper published in 1965, Penrose described how matter could collapse to form a black hole with a singularity at its center. More recently, British mathematician Roger Penrose won the 2020 Nobel Prize in physics for his calculations showing that black holes were real-world predictions of general relativity. The math showed a limit to how small a mass could be squeezed, an early sign of black holes. In 1916, Karl Schwarzschild published a solution to Einstein’s equations for general relativity near a single spherical mass. Mathematics has a history of big contributions in the realm of black holes. “Most of my work,” Giorgi says, “is about proving things that we already expected to be true.” If not, something is wrong with the underlying theory. If black holes are stable, as researchers presume, then the math describing them had better reflect that stability. Like a rubber band that has been stretched and then released, the black hole doesn’t rip apart, explode or cease to exist, but returns to something like its former self.īlack holes seem to be physically stable - otherwise they couldn’t endure in the universe - but proving it mathematically is a different beast.Īnd a necessary feat, Giorgi says.
A stable black hole, mathematically speaking, is one that if poked, nudged or otherwise disturbed will eventually settle back into being a black hole.
Last year, in a paper posted online at, Giorgi and colleagues settled a long-standing mathematical question about black hole stability. Mathematicians can solve equations that have bearing on questions about the nature of black holes’ formation, evolution and stability. Within general relativity, “one can understand clean mathematical statements and study those statements, and they can give an unambiguous answer within that theory,” says Christoph Kehle, a mathematician at ETH Zurich’s Institute for Theoretical Studies. “Most of my work,” Elena Giorgi says, “is about proving things that we already expected to be true.” April Renae/Columbia University Their goal: unlock unsuspected truths about black holes or verify existing suspicions. She and other mathematicians seek to prove theorems about these solutions and otherwise probe the math of general relativity. “Black holes are mathematical solutions to the Einstein equation,” Giorgi says - the “master equation” that is the basis of the general theory of relativity. Physicists have detected the X-rays emitted when black holes feed, analyzed the gravitational waves from black hole collisions and even imaged two of these behemoths.īut mathematician Elena Giorgi of Columbia University studies black holes in a different way.
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