In the following we consider the Kottler metric
with a constant and we ignore the region
for which the singularity at
is naked, for any value of
. For
, there is one horizon at a
radius
with
;
the staticity condition
is
satisfied on the region
. For
, there are two horizons at
radii
and
with
; the staticity condition
is
satisfied on the region
.
For
there is no horizon and no static
region. At the horizon(s), the Kottler metric can be analytically
extended into non-static regions. For
, the
resulting global structure is similar to the Schwarzschild case.
For
, the resulting global
structure is more complex (see [195]).
The extreme case
is discussed in [278].
For any value of , the Kottler metric
has a light sphere at
. Escape cones and embedding
diagrams for the Fermat geometry (optical geometry) can be found
in [314, 160
]
(cf. Figures 14
and 11
for the Schwarzschild
case). Similarly to the Schwarzschild spacetime, the Kottler
spacetime can be joined to an interior perfect-fluid metric with
constant density. Embedding diagrams for the Fermat geometry
(optical geometry) of the exterior-plus-interior spacetime can be
found in [315]. The
dependence on
of the light bending is discussed
in [194]. For the
optical appearance of a Kottler white hole see [196].
The shape of infinitesimally thin light bundles in the Kottler
spacetime is determined in [85].