Rigidity of the Spacetime Positive Mass Theorems
演讲者
时间
2024年09月09日 15:30 至 16:30
地点
Online
线上
Zoom 559 700 6085
(BIMSA)
摘要
In 1981, Schoen-Yau and Witten showed that in General Relativity, both the total energy E and the total mass m of an initial data set are non-negative.
In a joint work with Sven Hirsch, we show that if the total mass m=0, the initial data set must be contained in a pp-wave spacetime. Our proof combines spinorial methods with spacetime harmonic functions and works in all dimensions. Additionally, we find the decay rate threshold where the embedding has to be within Minkowski space and construct non-vacuum initial data sets with zero mass in the borderline case. As a consequence, this completely settles the rigidity of the spacetime positive mass theorems for spin manifolds.
In a joint work with Sven Hirsch, we show that if the total mass m=0, the initial data set must be contained in a pp-wave spacetime. Our proof combines spinorial methods with spacetime harmonic functions and works in all dimensions. Additionally, we find the decay rate threshold where the embedding has to be within Minkowski space and construct non-vacuum initial data sets with zero mass in the borderline case. As a consequence, this completely settles the rigidity of the spacetime positive mass theorems for spin manifolds.
演讲者介绍
我的研究方向是几何分析和广义相对论，目前主要研究标量曲率和广义相对论中的几何问题。我应用偏微分方程，特别是椭圆方程，来研究几何问题。