Hawking mass monotonicity for initial data sets

19.01.2023, 14:15-15:45  –  2.22 und Zoom
Geometric Analysis, Differential Geometry and Relativity

Sven Hirsch

An interesting feature of General Relativity is the presence of singularities which can happen in even the simplest examples such as the Schwarzschild spacetime. However, in this case the singularity is cloaked behind the event horizon of the black hole which has been conjectured to be generically the case. To analyze this so-called Cosmic Censorship Conjecture Penrose proposed in 1973 a test which involves Hawking's area theorem, the final state conjecture and a geometric inequality on initial data sets $$(M,g,k)$$. For $$k=0$$ this Penrose inequality has been proven by Huisken-Ilmanen and by Bray using different methods, but in general the question is wide open. Huisken-Ilmanen's proof relies on the Hawking mass monotonicity formula under inverse mean curvature flow (IMCF), and the purpose of this talk is to generalize the Hawking mass monotonicity formula to initial data sets. For this purpose, we start with recalling spacetime harmonic functions and their applications which have been introduced together with Demetre Kazaras and Marcus Khuri in the context of the spacetime positive mass theorem.