Uniqueness of (n+1)-dimensional black holes and equipotential photon surfaces in static vacuum

17.11.2022, 14:15-15:45  –  2.22 and Zoom
Geometric Analysis, Differential Geometry and Relativity

Albachiara Cogo (U Tübingen)

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.

This talk is part of the seminar Geometric Analysis, Differential Geometry and Relativity organized by Carla Cederbaum (Uni Tübingen), Melanie Graf (Uni Tübingen), and Jan Metzger (Uni Potsdam) . To obtain the Zoom data please contact jan.metzger@uni-potsdam.de