Frame-dragging vortexes and tidal tendexes attached to colliding black holes: Visualizing the curvature of spacetime
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. © 2011 American Physical Society.