David Fajman: Dynamics of General Relativity 4

Summer School »Between Geometry and Relativity«, Part 22: David Fajman: Dynamics of General Relativity 4

Abstract: The lectures discuss dynamical properties of solutions to the Einstein equations: On a suitable foliation of spacetime the Einstein equations take the form of a geometric flow: a system of hyperbolic PDEs that describes the evolution of a metric and a second fundamental form on a given 3-manifold. We outline one particular approach to resolve the local-existence problem for this geometric flow and apply this to study the global existence problem and stability of some cosmological spacetimes. Eventually, we give an overview on major results and open problems in this area.
David Fajman is a member of the workgroup "Gravitationsphysik" at U Vienna.

1. Lead 00:00:00
2. Recalling. Rescaling the variables 00:00:10
3. Perturbed quantities compared to the background 00:08:53
4. Elliptic estimates 00:17:06
5. Energy tensor for the wave equation. Conclusion 00:25:25