Hawking-Ellis classification of stress-energy tensors: Test fields versus backreaction

We consider the Hawking-Ellis (Segre-Plebanski) classification of stress-energy tensors, both in test-field limit, and presence back-reaction governed by usual Einstein equations. For test fields it is not too difficult to get a type~IV via quantum vacuum polarization effects. (For example, Unruh state for massless scalar field Schwarzschild background.) However, driven ordinary equations situation often much more constrained. instance: (1) any static spacetime always type I domain outer communication, on horizon that might be present; (2) stationary axisymmetric (3) Killing extendable bifurcation 2-surface I; (4) axis symmetry; (5) some homogeneous Bianchi cosmologies are guaranteed (for all cosmologies, FLRW "single mode" cosmologies). That is, very many physically interesting situations once one includes unusual types automatically excluded.