EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes

Abstract

In order to invariantly characterise spacetimes resulting from cosmological simulations in numerical relativity, we present two different methodologies to compute the electric and magnetic parts of the Weyl tensor, $E_{\alpha \beta }$ and $B_{\alpha \beta }$, from which we construct scalar invariants and the Weyl scalars. The first method is geometrical, computing these tensors in full from the metric, and the second uses the 3+1 slicing formulation. We developed a code for each method and tested them on five analytic metrics, for which we derived $E_{\alpha \beta }$ and $B_{\alpha \beta }$ and the various scalars constructed from them with computer algebra software. We find excellent agreement between the analytic and numerical results. The slicing code outperforms the geometrical code for computational convenience and accuracy; on this basis we make it publicly available in github with the name EBWeyl [ https://github.com/robynlm/ebweyl ]. We emphasize that this post-processing code is applicable to numerical spacetimes in any gauge.

42 pages, 10 figures, 2 appendices, EBWeyl can be found at https://github.com/robynlm/ebweyl V2: slightly improved version

References in corpus (17)

• Relativistic cosmology and large-scale structure
• Nonlinearities in Black Hole Ringdowns
• Nonlinear effects in black hole ringdown
• Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity
• Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
• Gravitational Waves from Nonlinear Couplings of Radial and Polar Nonradial Modes in Relativistic Stars
• A Concise Introduction to Perturbation Theory in Cosmology
• Einstein's signature in cosmological large-scale structure
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology
• Cosmology on all scales: a two-parameter perturbation expansion
• Cosmological nonlinear structure formation in full general relativity
• The Magnetic Part of the Weyl Tensor, and the Expansion of Discrete Universes
• Fully relativistic nonlinear cosmological evolution in spherical symmetry using the BSSN formalism
• Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions
• The halo bias for number counts on the light cone from relativistic N-body simulations
• Geometric horizons in binary black hole mergers
• Master Functions and Equations for Perturbations of Vacuum Spherically-Symmetric Spacetimes

Cited by in corpus (3)

• Cosmology using numerical relativity
• Gauge/frame invariant variables for the numerical relativity study of cosmological spacetimes
• Structure formation and quasi-spherical collapse from initial curvature perturbations with numerical relativity simulations