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 ). The extreme case is discussed in .
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 [313, 159] (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 . The dependence on of the light bending is discussed in . For the optical appearance of a Kottler white hole see . The shape of infinitesimally thin light bundles in the Kottler spacetime is determined in .
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