Math 753. Topics in Mathematical Physics: General Relativity
- Fall 10 - Hans Lindblad

First we will introduce Einstein's equations and try to motivate them from a physical and geometric point of view. The formulation of the equations requires geometric concepts, like tensors and curvature, which we will review. Einstein's equations describe how space curves under the influence of gravity. We will motivate the equations by studying the Newtonian approximation, special relativity, matter models and special solutions like cosmological space times and the Schwarzschild solution.

Then we will study how solutions of Einstein's equations behave. We will show that the initial value problem for Einstein's equations has a local unique solution (in harmonic coordinates). We will also show that Einstein's equations have global solutions (in harmonic coordinates) if initial conditions are close to flat space, as in my recent work with Rodnianski. Einstein's equation in harmonic coordinates become a system of nonlinear wave equations. We will therefore develop the tools needed to show existence and estimates for nonlinear wave equations.



It is also useful to first read a physics undergraduate/graduate text book like Carroll "Spacetime and Geometry".

The lectures are MW 1.30-2.45 in Krieger 304.

wk  date  Monday  Wednesday  Friday
  1  8/30 Introduction-Overview    
  2  9/6  Holiday    
  3  9/13  No Class  No Class  No Class
  4  9/20      No Class
  5  9/27      No Class
  6  10/4      No Class
  7  10/11  moved to Tuesday 10/12    No Class
  8  10/18    Tuesday 10/19 10.30 Shaffer 304  No Class
  9  10/25  Prof. Sogge lecture  Prof. Sogge lecture  No Class
10  11/1  Tuesday 11/2 10.30 Shaffer 304    
11  11/8      
12  11/15      
13  11/22    No Class  No Class
14  11/29