  Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the
electric and magnetic parts of the Weyl curvature tensor, form the basis of a
recently developed approach to visualizing spacetime curvature. In analogy to
electric and magnetic fields, these fields are coordinate-dependent. However,
in a further analogy, we can form invariants from the tendex and vortex fields
that are invariant under coordinate transformations, just as certain
combinations of the electric and magnetic fields are invariant under coordinate
transformations. We derive these invariants, and provide a simple, analytical
demonstration for non-spherically symmetric slices of a Schwarzschild
spacetime.
