The potential energy tensors for subsystems

An extension of Chandrasekhar's tensor virial theorem for one subsystem distorted by the tidal potential induced by another subsystem is formulated, with the possibility to extend the results to the tidal potential induced by any number of subsystems. To this aim, the self-energy tensor, the interaction-energy tensor, the tidal-energy tensor, and the residual-energy tensor are defined for each subsystem. The above mentioned quantities are evaluated for the special case of homogeneous, coaxial ellipsoids, one lying completely within the other. Concerning the special case of spheroids, a comparison is made with the results of previous approaches.