Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
Abstract
When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part Ejk that describes tidal gravity and a "magnetic" part Bjk that describes differential dragging of inertial frames. We introduce tools for visualizing Bjk (frame-drag vortex lines, their vorticity, and vortexes) and Ejk (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.
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