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Here’s a peek into the mathematics of black holes

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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.

A photo of Elena Giorgi standing in front of a blackboard with mathematical equations written in white chalk.
“Most of my work,” Elena Giorgi says, “is about proving things that we already expected to be true.”April Renae/Columbia University

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…

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