Andrea Nerozzi

CENTRA - Instituto Superior Técnico

The Newman-Penrose formalism and its use in numerical relativity

The recent breakthroughs in numerical relativity have made it possible to generate gravitational wave signals coming from binary systems. Most groups in numerical relativity use the Newman-Penrose formalism and in particular the Weyl scalar Ψ₄ to extract the information about gravitational waves from numerically generated space-times. Ψ₄ is calculated by contracting the Weyl tensor with a tetrad of null vectors, the choice of which constitutes the real gauge degree of freedom in this formalism. The optimal tetrad to calculate Ψ₄ constitutes an interesting and challenging problem from both analytical and numerical points of view. The condition that we want to satisfy is that Ψ₄ in the linear regime coincides with the corresponding value coming from perturbation theory and the Teukolsky master equation. In this work we present a compact expression for Ψ₄ that automatically enforces this condition, the result being a simple function of curvature invariants that can be easily calculated in a numerical code.