Action principle for Numerical Relativity evolution systems

Understand

A Lagrangian density is provided, that allows to recover the Z4 evolution system from an action principle.

• The resulting system is then strongly hyperbolic when supplemented by gauge conditions like '1+log' or 'freezing shift', suitable for numerical evolution.
• The physical constraint $Z_\mu = 0$ can be imposed just on the initial data.
• The corresponding canonical equations are also provided.