  The (generalized) Rainich conditions are algebraic conditions which are
polynomial in the (mixed-component) stress-energy tensor. As such they are
logically distinct from the usual classical energy conditions (NEC, WEC, SEC,
DEC), and logically distinct from the usual Hawking-Ellis (Segr\'e-Pleba\'nski)
classification of stress-energy tensors (type I, type II, type III, type IV).
There will of course be significant inter-connections between these
classification schemes, which we explore in the current article. Overall, we
shall argue that it is best to view the (generalized) Rainich conditions as a
refinement of the classical energy conditions and the usual Hawking-Ellis
classification.
