Stellar potential-energy tensor ($W_{ij}=-\int \rho x_i{\partial }_j\Phi d^{3}x$)

This force-moment tensor enters the tensor virial theorem. For an isolated self-gravitating population it is symmetric by pairwise interchange of the Newtonian interaction; for a tracer in an external field use the force-moment definition directly, with the appropriate symmetric combination in a time-dependent inertia identity.