Spin coefficients and gauge fixing in the Newman-Penrose formalism

Abstract

Since its introduction in 1962, the Newman-Penrose formalism has been widely used in analytical and numerical studies of Einstein's equations, like for example for the Teukolsky master equation, or as a powerful wave extraction tool in numerical relativity. Despite the many applications, Einstein's equations in the Newman-Penrose formalism appear complicated and not easily applicable to general studies of spacetimes, mainly because physical and gauge degrees of freedom are mixed in a nontrivial way. In this paper we approach the whole formalism with the goal of expressing the spin coefficients as functions of tetrad invariants once a particular tetrad is chosen. We show that it is possible to do so, and give for the first time a general recipe for the task, as well as an indication of the quantities and identities that are required.

12 pages, to match version published in PRD

References in corpus (6)

• Extraction of Gravitational Waves in Numerical Relativity
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
• On a five-dimensional version of the Goldberg-Sachs theorem
• A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad
• Scalar functions for wave extraction in numerical relativity

Cited by in corpus (5)

• A Review of Gravitational Memory and BMS Frame Fixing in Numerical Relativity
• Extending Gravitational Wave Extraction Using Weyl Characteristic Fields
• Tidal heating in a Riemann-Cartan spacetime
• Conformal Wavefunctions for Graviton Amplitudes
• Local and Approximate classification of spacetimes in the transverse frames