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    Null geodesics and embedding diagrams of the interior Schwarzschild-de Sitter spacetimes with uniform density

    Zdeněk Stuchlík · Srpen 01, 2001 · Fyzika · 0 comments
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    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;

    https://ui.adsabs.harvard.edu/abs/2001PhRvD..64d4004S

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