Analytical Tendex and Vortex Fields for Perturbative Black Hole Initial Data

TL;DR

This paper applies the tendex and vortex field visualization method to analytical initial data of black holes, offering insights into spacetime curvature and aiding future numerical simulations of black hole mergers.

Contribution

It introduces an analytical approach to compute tendex and vortex fields for perturbed black hole initial data, bridging the gap between theory and numerical relativity.

Findings

Provides analytical expressions for tendex and vortex fields in black hole initial data.

Demonstrates the method's applicability to both single and binary black holes.

Offers a benchmark for testing numerical relativity codes.

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.