Visualizing the Curvature of Spacetime: Vortex and Tendex Lines of Head-On Merging Binary Black Hole Systems*

A black hole forms when a massive star can no longer support the thermonuclear processes in its core that hold it up against its gravity. Inside a black hole's horizon, nothing can escape. Merging black holes and the gravitational waves---ripples of curved spacetime---they emit are the most promising sources for gravitational-wave detectors like Advanced LIGO. When black holes merge, the spacetime around them becomes curved in a dynamic, turbulent way, like a storm in spacetime. In this project, we use analogs of electric and magnetic field lines to visualize the curved spacetime of merging black holes. A non-spinning black hole will produce Tendicity; along tendex lines (analogs of electric field lines), objects are stretched and squeezed. A spinning black hole will produce Tendicity but will also twist the spacetime around it, producing vorticity; along vortex lines (analogs of magnetic field lines), objects are twisted. We produce simulations and visualizations of equal mass black hole merging with no spin, and produce visualizations of vortex and tendex lines showing how the curved spacetime behaves as the holes merge. The intent is to gain some intuition of the dynamics of spacetime around binary black holes.