The geodesic deviation equation tells us what tidal forces freely falling observers experience in a local Lorentz reference frame. The tidal deformation tensor is $$E^{\alpha}_{\gamma}=R^{\alpha}_{\beta\gamma\delta}U^{\beta}U^{\delta}$$ where $R^{\alpha}_{\beta\gamma\delta}$ is the Riemann curvature tensor and $U^{\alpha}$ is the four velocity along a timelike geodesic.
Are the eigenvalues of this tensor (expressed in an orthonormal basis) necessarily infinite at a singularity and bounded at a coordinate singularity? Are the eigenvalues related to scalar curvature invariants in any way? I am particularly interested if this may be useful to characterise vacuum spacetimes.
