Proposed 15 years ago, the bounded L2 curvature conjecture has finally been proved by a group of three researchers at the Laboratoire Jacques-Louis Lions (CNRS / UPMC / Université Paris Diderot) and Princeton University. It provides a potentially minimal framework in which it is possible to solve the Einstein equations, which in turn could be a critical step toward the proof of major conjectures, such as Penrose's cosmic censorship conjectures. This work has appeared in Inventiones Mathematicae on October 14.
Even though this year marks its 100th anniversary, Albert Einstein's theory of general relativity still holds its share of mysteries. This theory of gravitation stipulates that matter curves spacetime in proportion to the mass of the object. This phenomenon is measured using a mathematical tool called the curvature tensor, on which the bounded L2 curvature conjecture focuses to find possible frameworks for making sense of solutions to Einstein's equations. Proposed 15 years ago by Sergiu Klainerman, this conjecture has at last been demonstrated by Sergiu Klainerman, Igor Rodnianski and Jérémie Szeftel.
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