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;