Black branes and black strings in the astrophysical and cosmological
  context
  We consider Kaluza-Klein models where internal spaces are compact flat or
curved Einstein spaces. This background is perturbed by a compact gravitating
body with the dust-like equation of state (EoS) in the external/our space and
an arbitrary EoS parameter $\Omega$ in the internal space. Without imposing any
restrictions on the form of the perturbed metric and the distribution of the
perturbed energy densities, we perform the general analysis of the Einstein and
conservation equations in the weak-field limit. All conclusions follow from
this analysis. For example, we demonstrate that the perturbed model is static
and perturbed metric preserves the block-diagonal form. In a particular case
$\Omega=-1/2$, the found solution corresponds to the weak-field limit of the
black strings/branes. The black strings/branes are compact gravitating objects
which have the topology (four-dimensional Schwarzschild spacetime)$\times$
($d$-dimensional internal space) with $d\geq 1$. We present the arguments in
favour of these objects. First, they satisfy the gravitational tests for the
parameterized post-Newtonian parameter $\gamma$ at the same level of accuracy
as General Relativity. Second, they are preferable from the thermodynamical
point of view. Third, averaging over the Universe, they do not destroy the
stabilization of the internal space. These are the astrophysical and
cosmological aspects of the black strings/branes.
