  $\Lambda^{\mu}_{\nu}$-geometry is a geometry with a variable cosmological
term described by a second-rank symmetric tensor $\Lambda^{\mu}_{\nu}$ whose
asymptotics are Einstein cosmological term $\Lambda \delta ^{\mu}_{\nu}$ at the
origin and $\lambda \delta ^{\mu}_{\nu}$ at infinity (with $\lambda <
\Lambda$).
  It corresponds to extension of the algebraic structure of the Einstein
cosmological term $\Lambda \delta ^{\mu}_{\nu}$ in such a way that a scalar
$\Lambda$ describing vacuum energy density as $\rho_{vac}=8\pi G \Lambda$ (with
$\rho_{vac}$=const by virtue of the Bianchi identities), becomes explicite
related to the appropriate component, $\Lambda^0_0$, of an appropriate
stress-energy tensor, $T^{\mu}_{\nu}=8\pi G\Lambda^{\mu}_{\nu}$ whose vacuum
properties follow from its symmetry, $T_0^0=T_1^1$, and whose variability
follows from the contracted Bianchi identities. In the spherically symmetric
case existence of such geometries in frame of GR follows from imposing on
Einstein equations requirements of finiteness of the ADM mass $m$, and of
regularity of density and pressures. Dependently on parameters $m$ and
$q=\sqrt{\Lambda /\lambda}$, $\Lambda^{\mu}_{\nu}$ geometry describes five
types of configurations. We summarize here the results which tell us how these
configurations look from the point of view of different observers: a static
observer, a Lemaitre co-moving observer, and a Kantowski-Sachs observer.
