The Penrose Inequality with non-optimal constant
演讲者
Demetre Kazaras
时间
2025年05月13日 09:00 至 10:00
地点
Tsinghua-Jingzhai-105
线上
Zoom 204 323 0165
(BIMSA)
摘要
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.