Almost-stationary motions and gauge conditions in general relativity

An almost-stationary gauge condition is proposed with a view to numerical relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is derived from a variational principle, by minimizing the deviations from isometry. The corresponding almost-stationary gauge condition allows us to put the field equations in hyperbolic form, both in the free-evolution ADM and in the Z4 formalisms.