Geodesic Killing orbits and bifurcate Killing horizons

Abstract
Geodesic orbits of a one-dimensional groupGof isometries of a semi-Riemannian manifold are classified into complete and incomplete orbits. It is shown that the latter (which are null), if extendable, define fixed points ofG. A bifurcate Killing horizonN̂in a four-dimensional Lorentz manifold is defined as the union of intersecting (smooth) Killing horizons (of the same groupG). By means of an analysis of the action ofGnear a fixed point, the theorem is established that a Killing horizonNis contained, as a ‘branch’, in a bifurcate Killing horizonN̂if and only if it contains an incomplete, extendable, null geodesic orbit. Examples in familiar relativistic space times are pointed out.

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