Visualizing the Weyl Curvature Tensor: Frame-Drag Vortex Lines and Tidal Tendex Lines

When one slices spacetime into space plus time, the Weyl curvature tensor gets split into two symmetric, trace-free tensors: its ``electric'' part, which describes tidal forces, and its ``magnetic'' part, which describes differential frame dragging. The electric part is completely characterized by {\it tidal tendex lines} (integral curves of its eigenvectors) and their {\it tendicities} (eigenvalues); and the magnetic part, by corresponding {\it frame-drag vortex lines} and their {\it vorticities}. We will discuss the physical meanings of these quantities and their use to visualize spacetime curvature, and we will illustrate them for stationary situations: a spinning body in linearized theory, and a Kerr black hole.