EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes

TL;DR

This paper introduces two methods to compute invariant scalar quantities from the Weyl tensor in numerical relativity, with a publicly available code that performs well across different gauges.

Contribution

The paper presents two novel methodologies for invariant characterization of spacetimes in numerical relativity, including a publicly available, gauge-agnostic code.

Findings

The slicing-based method outperforms the geometrical method in accuracy and efficiency.

The code accurately reproduces analytic results for test metrics.

The approach is applicable to any gauge in 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.