# Geometric Analysis and Topology Seminar

#### Hawking mass monotonicity for initial data sets

**Speaker:**
Sven Hirsch, Institute for Advanced Studies (IAS)

**Location:**
Warren Weaver Hall 512

**Date:**
Friday, November 3, 2023, 11 a.m.

**Synopsis:**

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 so-called Penrose inequality has been proven by Huisken-Ilmanen via inverse mean curvature flow and by Bray using the conformal flow, but in general the question is wide open. We will present several appraoches to generalize the Hawking mass monotonicity formula to arbitrary initial data sets including a new one based on double null foliations. 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.