Seminar series
Date
Thu, 26 Feb 2015
Time
12:00 -
13:00
Location
L6
Speaker
Cecile Huneau
Organisation
Ecole Normale Superieure
In the presence of a translation space-like Killing field the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein equations with a scalar field. We work in generalised wave coordinates. In this gauge Einstein equations can be written as a system of quaslinear quadratic wave equations. The main difficulty is due to the weak decay of free solutions to the wave equation in 2 dimensions. To prove long time existence of solutions, we have to rely on the particular structure of Einstein equations in wave coordinates. We also have to carefully choose the behaviour of our metric in the exterior region to enforce convergence to Minkowski space-time at time-like infinity.