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.

arXiv comment12 pages, to match version published in PRD

References in corpus (23)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• Classification of the Weyl Tensor in Higher Dimensions
• Extraction of Gravitational Waves in Numerical Relativity
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Ricci identities in higher dimensions
• The Lazarus Project. II. Spacelike extraction with the quasi-Kinnersley tetrad
• Making use of geometrical invariants in black hole collisions
• Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
• Towards wave extraction in numerical relativity: the quasi-Kinnersley frame
• Towards a novel wave-extraction method for numerical relativity. I. Foundations and initial-value formulation
• Hyperbolic Equations for Vacuum Gravity Using Special Orthonormal Frames
• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• On a five-dimensional version of the Goldberg-Sachs theorem
• A Radiation Scalar for Numerical Relativity
• A hyperbolic tetrad formulation of the Einstein equations for numerical relativity
• Towards a wave-extraction method for numerical relativity: IV. Testing the quasi-Kinnersley method in the Bondi-Sachs framework
• A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad
• The perturbation theory of higher dimensional spacetimes a la Teukolsky
• Schwarzschild Tests of the Wahlquist-Estabrook-Buchman-Bardeen Tetrad Formulation for Numerical Relativity
• 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