Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime

TL;DR

This paper introduces visualization tools for spacetime curvature components, specifically tidal and frame-drag fields, to better understand the complex dynamics during black hole mergers.

Contribution

It presents novel visualization techniques for the electric and magnetic parts of the Weyl tensor, aiding in understanding black hole binary interactions.

Findings

Visualizations reveal the structure of vortexes and tendexes during mergers

Tools clarify the nonlinear spacetime dynamics in black hole collisions

Horizon vorticity and tendicity visualizations enhance understanding of horizon physics

Abstract

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E_{jk} that describes tidal gravity and a "magnetic" part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.