General Relativity Program Minicourses
During the Spring 2022 semester, the CMSA hosted a program on General Relativity.
This semester-long program included four minicourses running in March, April, and May; a conference April 4–8, 2022; and a workshop from May 2–5, 2022.
|March 1 – 3, 2022
10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
|Dr. Stefan Czimek
|Characteristic Gluing for the Einstein Equations
|Abstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface. Then we turn to bifurcate characteristic gluing (i.e. gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).
|March 22 – 25, 2022
22nd & 23rd, 10:00 am – 11:30am ET
24th & 25th, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room, G-10.
|Prof. Lan-Hsuan Huang
|Existence of Static Metrics with Prescribed Bartnik Boundary Data
|Abstract: 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
Video on Youtube: March 22, 2022
|March 29 – April 1, 2022 10:00am – 12:00pm ET, each day
Location: Hybrid. CMSA main seminar room, G-10.
|Prof. Martin Taylor
|The nonlinear stability of the Schwarzschild family of black holes
|Abstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.
|April 19 & 21, 2022
10 am – 12 pm ET, each dayZoom only
|Prof. Håkan Andréasson
|Two topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.
|Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole.
|May 16 – 17, 2022
10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
|Prof. Marcelo Disconzi
|A brief overview of recent developments in relativistic fluids
|Abstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity.
1. Set-up, review of standard results, physical motivation.