Free Evolution

Abstract

As we mentioned in the previous chapter, the “free evolution” approach is by far the most commonly used today in Numerical Relativity codes. It consists on using just the evolution equations to compute the full set of dynamical quantities (γ_ij,K_ij). We have seen that the subset of evolution equations is not unique: evolution equations can be modified by adding constraints in many different ways. This implies that we must distinguish among different versions of free evolution, depending on the particular variant of the evolution equations which is selected in each case. The first choice is to take just the space components of the four-dimensional Ricci tensor, namely