CMSA General Relativity Program: Existence of Static Metrics with Prescribed Bartnik Boundary Data
CMSA GENERAL RELATIVITY SEMINAR, SEMINARS
Speaker:
Profssor Lan-Hsuan Huang
The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is
1. The conjecture and an overview of the results
2. Static regular: a sufficient condition for existence and local uniqueness
3. Convex boundary, isometric embedding, and static regular
4. Perturbations of any hypersurface are static regular
March 22 – 25, 2022
22nd & 23rd, 10:00 am – 11:30am ET
24th & 25th, 11:00 am – 12:30pm ET
Location: Hybrid. CMSA main seminar room, G-10. Zoom link will be available.
All in-person attendees must register online.
For more information, please see https://cmsa.fas.harvard.edu/gr-program/