Degeneracy measures for the algebraic classification of numerical spacetimes

Abstract

We study the issue of algebraic classification of the Weyl curvature tensor, with a particular focus on numerical relativity simulations. The spacetimes of interest in this context, binary black hole mergers, and the ringdowns that follow them, present subtleties in that they are generically, strictly speaking, Type I, but in many regions approximately, in some sense, Type D. To provide meaning to any claims of "approximate" Petrov class, one must define a measure of degeneracy on the space of null rays at a point. We will investigate such a measure, used recently to argue that certain binary black hole merger simulations ring down to the Kerr geometry, after hanging up for some time in Petrov Type II. In particular, we argue that this hangup in Petrov Type II is an artefact of the particular measure being used, and that a geometrically better-motivated measure shows a black hole merger produced by our group settling directly to Petrov Type D.

14 pages, 7 figures. Version 2 adds two references.

References in corpus (6)

• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• Introduction to dynamical horizons in numerical relativity
• An intrinsic characterization of the Kerr metric
• The Final Remnant of Binary Black Hole Mergers: Multipolar Analysis
• A new method to compute quasi-local spin and other invariants on marginally trapped surfaces
• Scalar functions for wave extraction in numerical relativity

Cited by in corpus (16)

• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• The SXS Collaboration catalog of binary black hole simulations
• The Kerr Metric
• The RIT binary black hole simulations catalog
• Remnant of binary black-hole mergers: New simulations and peak luminosity studies
• On choosing the start time of binary black hole ringdown
• Spin flips in generic black hole binaries
• Intermediate-mass-ratio black hole binaries II: Modeling Trajectories and Gravitational Waveforms
• Accuracy Issues for Numerical Waveforms
• Extending Gravitational Wave Extraction Using Weyl Characteristic Fields
• Comparing Remnant Properties from Horizon Data and Asymptotic Data in Numerical Relativity
• A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad
• Multipole moments on the common horizon in a binary-black-hole simulation
• Seeking for toroidal event horizons from initially stationary BH configurations
• Falloff of the Weyl scalars in binary black hole spacetimes
• Local and Approximate classification of spacetimes in the transverse frames