Boundary Conditions

Abstract

Most Numerical Relativity simulations are devised to approximate the time evolution of the dynamical fields starting from data given on an initial time slice: the General Relativistic Cauchy or initial-value problem (IVP). The theoretical formalisms we have described so far are built with the objective of getting a well-posed Cauchy problem. This ensures, at the continuum level, that the solution is unique and depends smoothly on the initial data. A wellposed Cauchy problem is also a necessary condition for the existence of stable numerical algorithms that transpose the same property at the discrete level: the time evolution of the selected initial data must provide a sound approximation to the corresponding solution (the accuracy must improve with increasing numerical resolution).