Attendee ListScheduleView Videos

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 |