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Math: Mathematicians Disprove Conjecture Made to Save Black Holes

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Mathematicians have disproved the strong cosmic censorship conjecture. Their work answers one of the most important questions in the study of general relativity and changes the way we think about space-time.

Quanta Magazine said:
Nearly 40 years after it was proposed, mathematicians have settled one of the most profound questions in the study of general relativity. In a paper posted online last fall, mathematicians Mihalis Dafermos and Jonathan Luk have proven that the strong cosmic censorship conjecture, which concerns the strange inner workings of black holes, is false.

“I personally view this work as a tremendous achievement — a qualitative jump in our understanding of general relativity,” emailed Igor Rodnianski, a mathematician at Princeton University.

The strong cosmic censorship conjecture was proposed in 1979 by the influential physicist Roger Penrose. It was meant as a way out of a trap. For decades, Albert Einstein’s theory of general relativity had reigned as the best scientific description of large-scale phenomena in the universe. Yet mathematical advances in the 1960s showed that Einstein’s equations lapsed into troubling inconsistencies when applied to black holes. Penrose believed that if his strong cosmic censorship conjecture were true, this lack of predictability could be disregarded as a mathematical novelty rather than as a sincere statement about the physical world.

“Penrose came up with a conjecture that basically tried to wish this bad behavior away,” said Dafermos, a mathematician at Princeton University.

This new work dashes Penrose’s dream. At the same time, it fulfills his ambition by other means, showing that his intuition about the physics inside black holes was correct, just not for the reason he suspected.

Relativity’s Cardinal Sin

In classical physics, the universe is predictable: If you know the laws that govern a physical system and you know its initial state, you should be able to track its evolution indefinitely far into the future. The dictum holds true whether you’re using Newton’s laws to predict the future position of a billiard ball, Maxwell’s equations to describe an electromagnetic field, or Einstein’s theory of general relativity to predict the evolution of the shape of space-time. “This is the basic principle of all classical physics going back to Newtonian mechanics,” said Demetrios Christodoulou, a mathematician at ETH Zurich and a leading figure in the study of Einstein’s equations. “You can determine evolution from initial data.”

But in the 1960s mathematicians found a physical scenario in which Einstein’s field equations — which form the core of his theory of general relativity — cease to describe a predictable universe. Mathematicians and physicists noticed that something went wrong when they modeled the evolution of space-time inside a rotating black hole.

To understand what went wrong, imagine falling into the black hole yourself. First you cross the event horizon, the point of no return (though to you it looks just like ordinary space). Here Einstein’s equations still work as they should, providing a single, deterministic forecast for how space-time will evolve into the future.

But as you continue to travel into the black hole, eventually you pass another horizon, known as the Cauchy horizon. Here things get screwy. Einstein’s equations start to report that many different configurations of space-time could unfold. They’re all different, yet they all satisfy the equations. The theory cannot tell us which option is true. For a physical theory, it’s a cardinal sin.

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