Asymptotics of solutions in evolutionary formulations of the Einstein constraint equations.

Abstract

Performing a 2+1 split of an initial data set allows one to formulate the Einstein constraint equations as an initial value problem. There are two possible sets of equations that can arise here, the parabolic-hyperbolic equations and the strictly hyperbolic equations. The fundamental difference between the two formulations is in how the 2+1 lapse is treated. We study the asymptotic behaviour of solutions in both formulations by considering perturbations to known solutions of the constraint equations. The thesis then ends by introducing a model to produce data sets that describe binary black holes in the parabolic-hyperbolic formulations.