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Mass in General Relativity: March 26 – 30, 2018

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Workshop: Mass in General Relativity
March 26-30, 2018
Organized by: Piotr Chrusciel, Richard Schoen, Christina Sormani, Mu-Tao Wang, and Shing-Tung Yau

Due to the equivalence principle and the lack of an absolute space, the understanding of the fundamental notion of mass in general relativity has been subtle since Einstein’s time.  Arnowitt-Deser-Misner gave the well-defined definition for an asymptotically flat isolated system, while Bondi-Trautman gave the definition of mass after  gravitation radiation. By 1970’s, it was well-recognized that the positivity of these notions, which is intimately related to the stability of the system, lies in the foundation of the theory of general relativity.  There was an intense period of the study and the efforts culminated in the proof of the positive mass theorem by Schoen-Yau in 1980’s. The subject has since undergone rapid developments. Schoen-Yau’s proof led to the deeper understanding of initial data sets and trapped surfaces. Witten’s proof led to the notion of mass on asymptotically hyperbolic initial  data and the positivity.  Many new ideas and techniques from geometric analysis and physics emerge and are applied into the study.  The goal of this workshop is to provide a setting for the most cutting edge results to be presented, and to facilitate interaction among researchers. The topics include, but not limit to, the following:

1. Mass and boundary conditions: The notion of mass for asymptotically (A)dS space and the relation to the AdS/CFT correspondence.
The notion of Bondi-Trautman mass in higher dimensions.
The notion of quasi-local mass.

2. Inequalities involving mass: The spacetime Penrose inequality.
The mass-angular momentum inequality.

3. Mass and interior geometry: What does the mass defined at the (either finite or infinity) boundary tell us about the interior?
When the mass is small, the interior should be close to a flat space.
On the other hand, when the mass is large enough compared to other geometric data, black hole or trapped surface should form.
This is within the context of the hoop conjecture.

4. Mass and initial data set construction: Density theorems.
Center of mass and CMC foliations.

Talk Schedule


Time Title Presenter Location
10:00am Positive Mass Theorem in All Dimensions R Schoen SCGP 102
11:30am Lunch N/A Cafe
1:00pm Rigidity of the Positive Mass Theorem L-H Huang SCGP 102
2:30pm Quasi-local mass with reference in the static spacetimes and the rigidity of surfaces in the Schwarzschild manifold. P-N Chen SCGP 102
3:30pm Spacetime Intrinsic Flat Convergence and Mass C Sormani SCGP 102
4:00pm Tea N/A N/A
4:30pm Geometry of spacetime and mass in general relativity Mass in General Relativity: Public Lecture of Professor Shing-Tung Yau SCGP 103

Time Title Presenter Location
10:00am Einstein constraint equations: old and new A Carlotto SCGP 102
11:00am Coffee Break N/A Cafe
11:30am X Zhou Min-max theory for constant mean curvature (CMC) hypersurfaces SCGP 102
12:00pm Lunch N/A Cafe
1:00pm The mass of asymptotically hyperbolic manifolds P Chrusciel SCGP 102
2:30pm Minimal surfaces in asymptotically flat 3-manifolds O Chodosh SCGP 102
3:30pm Tea N/A N/A
4:00pm Geometric Inequalities for Near Maximal Axially Symmetric Initial Data Y-S Cha SCGP 102
5:15pm Quasilocal mass and isometric embedding M T Wang SCGP 102

Time Title Presenter Location
10:00am Universal positive mass theorems M Herzlich SCGP 102
11:00am Coffee Break N/A Cafe
11:30am Minimal hypersurface and boundary behavior of a compact manifold S Lu SCGP 102
12:00pm Lunch N/A Cafe
1:00pm Stationary Vacuum Black Holes in 5 Dimensions M Khuri SCGP 102
2:30pm  Nonlinear stability of self-gravitating massive P LeFloch SCGP 102
3:30pm Tea N/A N/A
4:00pm Null Geometry and the Penrose Conjecture H Roesch SCGP 102
5:15pm Deformation of mass aspect function and positive energy for asymptotically hyperbolic manifolds L Nguyen SCGP 102

Time Title Presenter Location
10:00am positive scalar curvature with singularities. C Mantoulidis SCGP 102
11:00am Coffee Break N/A Cafe
11:30am Minimal hypersurfaces with free boundary and positive scalar curvature bordism D Kazaras SCGP 102
12:00pm Lunch N/A Cafe
1:00pm A connection between Bartnik mass and Wang-Yau quasi-local mass P Miao SCGP 102
2:30pm “A generalized notion of ADM mass for static perfect fluids” A Burtscher SCGP 102
3:30pm Tea N/A N/A
4:00pm Relating relativistic point sources to continuous matter distributions I Stavrov SCGP 102
5:15pm Ricci flow on asymptotically Euclidean manifolds Yu Li SCGP 102
6:30pm Stability of the PMT and RPI using IMCF B Allen SCGP 102

Time Title Presenter Location
10:00am Gravitational waves: Interplay between physics and geometry. A Ashtekar SCGP 102
11:00am Coffee Break N/A Cafe
11:30am A geometric framework for cosmological spacetimes B Bonga SCGP 102
12:00pm Lunch N/A Cafe
1:00pm Minimizers of Bartnik’s quasi-local mass. J Jauregui SCGP102
2:30pm Extensions of Riemannian manifolds and Bartnik mass estimates A Cabrera SCGP 102
3:30pm Tea N/A N/A
4:00pm A rigidity theorem in negative scalar curvature, and some classification results in positive scalar curvature. L Ambrozio SCGP 102
5:00pm Mass in Kaehler Geometry C LeBrun SCGP 102