Hawking-Ellis type of matter on Killing horizons in symmetric spacetimes

Spherically, plane, or hyperbolically symmetric spacetimes with an additional hypersurface orthogonal Killing vector are often called ``static'' even if they contain regions where the is non-timelike. It seems to be widely believed that energy-momentum tenor for a matter field compatible these in general relativity of Hawking-Ellis type I everywhere. We show arbitrary $n(\ge 3)$ dimensions that, contrary popular belief, on horizon not necessarily but can II. Such type-II realized Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole Einstein-Maxwell-dilaton system and may interpreted as mixture particular anisotropic fluid null dust fluid.