A team of mathematicians based in Vienna is developing tools to extend the scope of general relativity.

In October 2015, a young mathematician named Clemens Sämann was flying home to Austria from a conference in Turin, Italy, when he had a chance encounter. He found himself seated beside Michael Kunzinger, another conference attendee. Kunzinger was a math professor at the University of Vienna, where Sämann had just started his postdoctoral research. They soon got to talking, landing on a subject Sämann had started thinking about in graduate school — whether there was a mathematical way to get around the limitations of Albert Einstein’s general theory of relativity.

Einstein’s theory defines gravity as the curvature of space-time caused by the presence of matter and energy. Since its formulation in 1915, it has held up remarkably well. Consisting of 10 interconnected differential equations, the theory describes how objects fall, how light bends, and how planets, stars and galaxies move. It tells us that the universe is expanding, and it predicted the existence of both black holes and gravitational waves a century before they were definitively observed.

But in spite of these successes, Einstein’s theory also has shortcomings. Its equations can only describe how matter curves space-time when the geometry of that space-time is smooth — with no sharp corners or cusps, no regions where it suddenly becomes jagged. Picture space-time as a flat rubber sheet, and matter as a bowling ball placed on that sheet, causing it to bend. If space-time is smooth, then this bending will be gradual.

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