Here’s A Peek Into The Mathematics Of Black Holes

Mathematician Elena Giorgi of Columbia University and others are trying to solve black holes using mathematics to solve the Einstein equation.

Black holes exist in our universe. That’s widely accepted today. 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.

But mathematician Elena Giorgi of Columbia University studies black holes in a different way. “Black holes are mathematical solutions to the Einstein equation,” Giorgi says — the “master equation” that is the basis of the general theory of relativity.

She and other mathematicians seek to prove theorems about these solutions and otherwise probe the math of general relativity. Their goal: unlock unsuspected truths about black holes or verify existing suspicions.

“Most of my work,” Elena Giorgi says, “is about proving things that we already expected to be true.”

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. Mathematicians can solve equations that have bearing on questions about the nature of black holes’ formation, evolution and stability.

Last year, in a paper posted online at, Giorgi and colleagues settled a long-standing mathematical question about black hole stability. A stable black hole, mathematically speaking, is one that if poked, nudged or otherwise disturbed will eventually settle back into being a black hole. 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.

Black holes seem to be physically stable — otherwise they couldn’t endure in the universe — but proving it mathematically is a different beast.

And a necessary feat, Giorgi says. If black holes are stable, as researchers presume, then the math describing them had better reflect that stability. If not, something is wrong with the underlying theory.

“Most of my work,” Giorgi says, “is about proving things that we already expected to be true.”

A study published in the journal Nature has forced astronomers to rethink how the universe works after the James Webb Space Telescope discovered six massive galaxies.

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