A New Geometry for Einstein’s Theory of Relativity
1 min read
Summary
Albert Einstein’s 1915 theory of general relativity revolutionized our understanding of gravity, correctly predicting phenomena from the universe’s expansion to the existence of black holes and gravitational waves.
But the equations underlying the theory break down whenever space-time doesn’t have a smooth geometry.
In 2015, the mathematician Clemens Sämann had a chance encounter with a colleague on a flight from Italy to Austria.
They wondered whether it might be possible to extend the boundaries of general relativity by developing alternative mathematical methods that would work in inhospitable settings.
Their methods estimate curvature and other geometric properties without assuming smoothness, and have helped reestablish important singularity theorems about black holes and the Big Bang.
Last year, Sämann and colleagues began developing ways to extend techniques from calculus to non-smooth settings — work that could eventually help underpin a theory of quantum gravity.
