Analytical Tendex and Vortex Fields for Perturbative Black Hole Initial Data

Abstract

Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the electric and magnetic parts of the Weyl curvature tensor, form the basis of a recently developed approach to visualizing spacetime curvature. In particular, this method has been proposed as a tool for interpreting results from numerical binary black hole simulations, providing a deeper insight into the physical processes governing the merger of black holes and the emission of gravitational radiation. Here we apply this approach to approximate but analytical initial data for both single boosted and binary black holes. These perturbative data become exact in the limit of small boost or large binary separation. We hope that these calculations will provide additional insight into the properties of tendex and vortex fields, and will form a useful test for future numerical calculations.

18 pages, 8 figures, submitted to PRD

References in corpus (13)

• Supermassive recoil velocities for binary black-hole mergers with antialigned spins
• Getting a kick out of numerical relativity
• Spin Flips and Precession in Black-Hole-Binary Mergers
• Understanding the "anti-kick" in the merger of binary black holes
• Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
• Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications
• Modeling maximum astrophysical gravitational recoil velocities
• Black-hole horizons as probes of black-hole dynamics I: post-merger recoil in head-on collisions
• Black-hole horizons as probes of black-hole dynamics II: geometrical insights
• Approximate initial data for binary black holes
• Trumpet-puncture initial data for black holes
• Classifying the Isolated Zeros of Asymptotic Gravitational Radiation by Tendex and Vortex Lines
• An alternative approach to solving the Hamiltonian constraint

Cited by in corpus (2)

• The SXS Collaboration catalog of binary black hole simulations
• Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates