A quick introduction to the Einstein equations

Monday, June 24, 2002 - 9:10am - 10:00am
Keller 3-180
Douglas Arnold (University of Minnesota, Twin Cities)
This talk is meant to give a fairly self-contained, quite formal, and very succinct introduction to the Einstein equations, including the required differential geometry and a choice of notational conventions. The equations will be first presented in an entirely coordinate-free manner emphasizing their geometric content, and then the corresponding PDEs satisfied by the metric components with respect to some coordinate system will be derived. The gauge freedom in the equations will be discussed both in the coordinate-free and the coordinatized context.