Visualizing the Weyl Curvature Tensor: Frame-Drag Vortex Lines and Tidal Tendex Lines
ORAL
Abstract
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.
*This work was supported by NSF grants PHY-0601459, PHY-0653653, PHY-0960291, PHY-0969111, PHY-1005426 and PHY-0956189; NASA grants NNX09AF97G and NNX09AF96G, the Sherman Fairchild and Brinson Foundations, and the David and Barbara Groce Fund
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