On the use of curvature invariants in numerical relativity

The recent breakthroughs in numerical relativity have made it possible to generate gravitational wave signals coming from binary systems. The waveforms are extracted using the Newman-Penrose formalism and in particular the Weyl scalar ψ 4 . In order for ψ 4 to contain the physical information on the gravitational wave signal, the tetrad chosen for its calculation should converge to the Kinnersley tetrad in the limit of single black hole space-time. In this work we present a compact expression for ψ 4 that automatically enforces this condition; the result is a simple function of curvature invariants that can be easily calculated in a numerical code.