The universe is not always smooth — at the centers of black holes, for instance, the curvature of space-time explodes to infinity, forming a singularity., Whenever space-time isn’t sufficiently smooth, the 10 interconnected differential equations underlying Albert Einstein’s general theory of relativity stop working.
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, and landed on Einstein’s general theory of relativity and its limitation to smooth space-times. They wondered whether there was a mathematical way to get around this limitation.
The pair wouldn’t start working on the problem in earnest for another year. But since then, they’ve made significant advances toward their goal. They’ve found new ways to estimate curvature and other geometric properties without relying on the assumption that space-time is smooth. In collaboration with other researchers, they’ve used their methods to rederive (and sometimes strengthen) core theorems about the universe without depending on Einstein’s equations, putting those theorems on even firmer mathematical footing.
And they’re now part of an ambitious new program — launched last year under the direction of Roland Steinbauer, another University of Vienna mathematician — that aims to provide “a new geometry for Einstein’s theory of relativity and beyond.”
“Standard general relativity talks about geometric objects, namely space-times, but only if they behave nicely enough,” Steinbauer said. “With this new framework, we can go beyond that. We can handle very edgy objects, very badly behaved objects.”
Quanta Magazine
The universe is not always smooth — at the centers of black holes, for instance, the curvature of space-time explodes to infinity, forming a singularity., Whenever space-time isn’t sufficiently smooth, the 10 interconnected differential equations underlying Albert Einstein’s general theory of relativity stop working.
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, and landed on Einstein’s general theory of relativity and its limitation to smooth space-times. They wondered whether there was a mathematical way to get around this limitation.
The pair wouldn’t start working on the problem in earnest for another year. But since then, they’ve made significant advances toward their goal. They’ve found new ways to estimate curvature and other geometric properties without relying on the assumption that space-time is smooth. In collaboration with other researchers, they’ve used their methods to rederive (and sometimes strengthen) core theorems about the universe without depending on Einstein’s equations, putting those theorems on even firmer mathematical footing.
And they’re now part of an ambitious new program — launched last year under the direction of Roland Steinbauer, another University of Vienna mathematician — that aims to provide “a new geometry for Einstein’s theory of relativity and beyond.”
“Standard general relativity talks about geometric objects, namely space-times, but only if they behave nicely enough,” Steinbauer said. “With this new framework, we can go beyond that. We can handle very edgy objects, very badly behaved objects.”
Read the full story: www.quantamagazine.org/a-new-geometry-for-einstein…
🎨Credit:
1: @harolbustos for Quanta Magazine
3: Der Knopfdrücker; Joseph Krpelan
4: @artscistudios/Quanta Magazine
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