BIMSA > Hyperbolic Mass The Penrose Inequality with non-optimal constant
The Penrose Inequality with non-optimal constant
Organizers
Shing-Tung Yau , Yiyue Zhang , Bowen Zhao
Speaker
Demetre Kazaras
Time
Tuesday, May 13, 2025 9:00 AM - 10:00 AM
Venue
Tsinghua-Jingzhai-105
Online
Zoom 204 323 0165 (BIMSA)
Abstract
To test the Weak Cosmic Censorship Hypothesis, Penrose proposed an inequality between the ADM mass $m$ of a spacetime and the cross-sectional area $A$ of its event horizon, which reads $16\pi m^2\geq A$. In this talk, we work with asymptotically flat initial data sets satisfying the dominant energy condition and show $C m^2>A_h$, where $A_h$ is the minimal area required to enclose an outermost apparent horizon and the (non-optimal) constant $C$ is less than $10^{18}$. The proof combines Schoen-Yau's analysis of the Jang equation, the harmonic function approach to the Positive Mass Theorem, and Dong-Song's stability argument. This is joint work with Brian Allen, Edward Bryden, and Marcus Khuri.