Abstract
Geodesic orbits of a one-dimensional group
G
of 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 of
G
. A bifurcate Killing horizon
N̂
in a four-dimensional Lorentz manifold is defined as the union of intersecting (smooth) Killing horizons (of the same group
G
). By means of an analysis of the action of
G
near a fixed point, the theorem is established that a Killing horizon
N
is contained, as a ‘branch’, in a bifurcate Killing horizon
N̂
if and only if it contains an incomplete, extendable, null geodesic orbit. Examples in familiar relativistic space times are pointed out.
Reference8 articles.
1. Bishop R . L. & C rittenden R . J . 1964 Geometry of manifolds. New Y ork: Academic Press.
2. C arter B. 1966 P hys. Rev. 1 4 1 1242.
3. J . M ath;Ellis G. F .;Phys.,1967
4. Hoffm ann B. (ed.) 1966 Perspectives in geometry and relativity. Bloom ington: Indiana U niversity Press.
5. Schrodinger E . 1956 E xpanding universes. Cam bridge U niversity Press.
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