Dynamical shift conditions for the Z4 and BSSN formalisms

A class of dynamical shift conditions is shown to lead to a pseudohyperbolic evolution system, both in the Z4 and in the BSSN numerical relativity formalisms. This is done by using a plane-wave analysis which can be viewed as an extension of the standard Fourier analysis for this kind of systems. The proposed class generalizes the harmonic shift condition, where light speed is the only nontrivial characteristic speed, and it is contained into the multiparameter family of minimal distortion shift conditions recently proposed by Lindblom and Scheel. The relationship with the analogous “dynamical freezing” shift conditions used in black hole simulations is discussed.