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

TL;DR

This paper demonstrates that matter fields on Killing horizons in symmetric spacetimes can be of Hawking-Ellis type II, challenging the common belief that they are always type I, with implications for black hole models.

Contribution

It proves that matter fields on Killing horizons can be of type II in arbitrary dimensions, contrary to the common assumption of type I, and provides explicit examples.

Findings

Matter fields on Killing horizons can be of type II.

Type-II matter fields include mixtures of anisotropic fluid and null dust.

Examples are found in Einstein-Maxwell-dilaton black holes.

Abstract

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