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When one splits spacetime into space plus time, the Weyl curvature tensor(which equals the Riemann tensor in vacuum) splits into two spatial, symmetric,traceless tensors: the tidal field $E$, which produces tidal forces, and theframe-drag field $B$, which produces differential frame dragging. In recentpapers, we and colleagues have introduced ways to visualize these two fields:tidal tendex lines (integral curves of the three eigenvector fields of $E$) andtheir tendicities (eigenvalues of these eigenvector fields); and thecorresponding entities for the frame-drag field: frame-drag vortex lines andtheir vorticities. These entities fully characterize the vacuum Riemann tensor.In this paper, we compute and depict the tendex and vortex lines, and theirtendicities and vorticities, outside the horizons of stationary (Schwarzschildand Kerr) black holes; and we introduce and depict the black holes' horizontendicity and vorticity (the normal-normal components of $E$ and $B$ on thehorizon). For Schwarzschild and Kerr black holes, the horizon tendicity isproportional to the horizon's intrinsic scalar curvature, and the horizonvorticity is proportional to an extrinsic scalar curvature. We show that, forhorizon-penetrating time slices, all these entities ($E$, $B$, the tendex linesand vortex lines, the lines' tendicities and vorticities, and the horizontendicities and vorticities) are affected only weakly by changes of slicing andchanges of spatial coordinates, within those slicing and coordinate choicesthat are commonly used for black holes. [Abstract is abbreviated.]

Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes