Publikace ÚTF

In this work we present and analyze a new class of coordinate representations of de Sitter and anti–
de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric.
Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1 þ 3
foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2 þ 2 foliation,
and are warped products of two 2-spaces of constant curvature. This new class of (anti–)de Sitter metrics
depends on the value of cosmological constant Λ and two discrete parameters þ1; 0; −1 related to the
curvature of the 2-spaces. The class admits 3 distinct subcases for Λ > 0 and 8 subcases for Λ < 0.
We systematically study all these possibilities. In particular, we explicitly present the corresponding
parametrizations of the (anti–)de Sitter hyperboloid, visualize the coordinate lines and surfaces
within the global conformal cylinder, investigate their mutual relations, present some closely related
forms of the metrics, and give transformations to standard de Sitter and anti–de Sitter metrics.
Using these results, we also provide a physical interpretation of B-metrics as exact gravitational fields of
a tachyon.