Newtonian tidal eigenvalues outside a point mass ($\mathrm{eig}T=(2,-1,-1)GM/r^3$)

For $\Phi =-GM/r$, the acceleration tidal tensor isIts radial eigenvalue is $2GM/r^3$ and its two transverse eigenvalues are $-GM/r^3$. This stretches a small freely falling cloud radially and compresses it transversely. The zero trace expresses the vacuum Poisson equation outside the source; within matter the trace is $-4\pi G\rho$.