Numerical investigations of the asymptotics of solutions to the evolutionary form of the constraints

Abstract

Systematic numerical investigations of the asymptotics of near Schwarzschild vacuum initial data sets is carried out by inspecting solutions to the parabolic-hyperbolic and to the algebraic-hyperbolic forms of the constraints, respectively. One of our most important findings is that the concept of near Schwarzschild configurations, applied previously in [4, 5], is far too restrictive. It is demonstrated that by relaxing the conditions on the freely specifiable part of the data a more appropriate notion of near Schwarzschild initial data configurations can be defined which allows us to generate asymptotically flat initial data configurations.

42 page, 12 figures