Black Strings from Minimal Geometric Deformation in a Variable Tension
  Brane-World
  We study brane-world models with variable brane tension and compute
corrections to the horizon of a black string along the extra dimension. The
four-dimensional geometry of the black string on the brane is obtained by means
of the minimal geometric deformation approach, and the bulk corrections are
then encoded in additional terms involving the covariant derivatives of the
variable brane tension. Our investigation shows that the variable brane tension
strongly affects the shape and evolution of the black string horizon along the
extra dimension, at least in a near-brane expansion. In particular, we apply
our general analysis to a model motivated by the E\"otv\"os branes, where the
variable brane tension is related to the Friedmann-Robertson-Walker brane-world
cosmology. We show that for some stages in the evolution of the universe, the
black string warped horizon collapses to a point and the black string has
correspondingly finite extent along the extra dimension. Furthermore, we show
that in the minimal geometric deformation of a black hole on the variable
tension brane, the black string has a throat along the extra dimension, whose
area tends to zero as time goes to infinity.
