In this joint work with Cederbaum, Leandro and Dos Santos, we generalize to any dimension n+1 Robinson’s divergence formula used to prove the uniqueness of (3+1)-dimensional static black holes. To this end, we use a tensor first introduced by Cao and Chen for the analysis and classification of Ricci solitons. We thereby prove the uniqueness of black holes and of equipotential photon surfaces in the class of asymptotically flat (n+1)-dimensional static vacuum space-times, provided the total scalar curvature of the horizon is properly bounded from above. In the black hole case, our results recover those of Agostiniani and Mazzieri and partially re-establish the results by Gibbons, Ida, and Shiromizu, and Hwang and finally by Raulot in the case of a spin manifold; in the photon surface case, the results by Cederbaum and Galloway can also be proven. Our proof is not based on the positive mass theorem and avoids the spin assumption.

Black Hole and Equipotential Photon Surface Uniqueness in (n+1)-dimensional Static Vacuum Spacetimes via Robinson's Method

In this talk, I want to give a pedagogical overview of Zhu's algebras and then describe an alternative approach to understanding their algebraic structure that has resurfaced in 3D-2D correspondences. First, I will introduce the approach to Zhu's algebras in physics and the resulting calculational framework. Following that, I'll describe the link between Zhu's algebras and Yangians and briefly discuss how these links are realised in physics if time permits.