**Publication date:** Aug 2001

**Abstract:**

Null geodesics and embedding diagrams of central planes in the ordinary

space geometry and the optical reference geometry of the interior

Schwarzschild-de Sitter spacetimes with uniform density are studied. For

completeness, both positive and negative values of the cosmological

constant are considered. The null geodesics are restricted to the

central planes of these spacetimes, and their properties can be

reflected by an „effective potential.“ If the interior spacetime is

extremely compact, the effective potential has a local maximum

corresponding to a stable circular null geodesic around which bound null

geodesics are concentrated. The upper limit on the size of the interior

spacetimes containing bound null geodesics is R=3M, independently of the

value of the cosmological constant. The embedding diagrams of the

central planes of the ordinary geometry into three-dimensional Euclidean

space are well defined for the complete interior of all spacetimes with

a repulsive cosmological constant, but the planes cannot be embedded

into the Euclidean space in the case of spacetimes with subcritical

values of an attractive cosmological constant. On the other hand, the

embedding diagrams of the optical geometry are well defined for all of

the spacetimes, and the turning points of these diagrams correspond to

the radii of the circular null geodesics. All the embedding diagrams,

for both the ordinary and optical geometry, are smoothly matched to the

corresponding embedding diagrams of the external vacuum Schwarzschild-de

Sitter spacetimes.

**Authors:**

Stuchlík, Zdeněk.; Hledík, Stanislav; Šoltés, Jiří.; Østgaard, Erlend;