Essential core of the Hawking--Ellis types

Understand

The Hawking-Ellis (Segre-Plebanski) classification of possible stress-energy tensors is an essential tool in analyzing the implications of the Einstein field equations in a more-or-less model-independent manner.

• In the current article the basic idea is to simplify the Hawking-Ellis type I, II, III, and IV classification by isolating the "essential core" of the type II, type III, and type IV stress-energy tensors; this being done by subtracting (special cases of) type I to simplify the (Lorentz invariant) eigenvalue structure as much as possible without disturbing the eigenvector structure.
• We will denote these "simplified cores" type II$_0$, type III$_0$, and type IV$_0$.
• These "simplified cores" have very nice and simple algebraic properties.