Further interpretation and application of frame-drag vorticity and tidal tendicity

Previous talks in this session presented concepts of frame-drag vorticity and tidal tendicity in the bulk spatial slices in curved spacetimes. Analogous concepts can be defined directly on two-surfaces, such as slices of black hole horizons, defining ``horizon vortexes'' and ``horizon tendexes.'' I will discuss these concepts, their relationship to the piercing of the two-surface by the vortex lines and tendex lines, to the geometry (intrinsic and extrinsic) of the two-surface, and to existing constructions defining black hole spin and other source multipoles. I will also present simulations of equal-mass black hole binaries in the so-called ``extreme kick'' configuration carried out recently with the SpEC code, and interpret the maximization of the kick in terms of these concepts of vorticity and tendicity.