Rigidity of the Spacetime Positive Mass Theorems
Organizers
Speaker
Time
Monday, September 9, 2024 3:30 PM - 4:30 PM
Venue
Online
Online
Zoom 559 700 6085
(BIMSA)
Abstract
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.
Speaker Intro
I am interested in geometric analysis and general relativity. More specifically, I am working on problems related to scalar curvature and geometric problems from physics. I enjoy applying the tools from PDEs, especially elliptic PDEs, to study geometry.