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Chiral connection formalism for GR and a new local rigidity result for Einstein 4-manifolds
Mathematical Physics Seminar| Speaker: | Kirill Krasnov, Nottingham |
| Location: | 918 3509 0938 Zoom o verse |
| Start time: | Fri, May 14 2021, 11:00AM |
I will start by reviewing how in four dimensions, when the scalar curvature is non-vanishing, the Einstein condition for a Riemannian signature metric can be encoded in certain second order PDE's on an SO(3) connection. When these PDE's are satisfied, the connection gets identified with the chiral half of the spin connection. The PDE's in question arise as Euler-Lagrange equations following by extremising a certain action functional. On some Einstein 4-manifolds, this functional can be shown to be (locally) convex, which is very different from the Einstein-Hilbert functional that is never convex. This can be used to establish a new "chiral" local rigidity result for Einstein 4-manifolds. The new result imposes a condition on only one of the two chiral halves of the Weyl curvature and in this sense is twice stronger than the previously available result.
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