Black strings from minimal geometric deformation in a variable tension brane-world

Abstract

We study brane-world models with variable brane tension and compute\ncorrections to the horizon of a black string along the extra dimension. The\nfour-dimensional geometry of the black string on the brane is obtained by means\nof the minimal geometric deformation approach, and the bulk corrections are\nthen encoded in additional terms involving the covariant derivatives of the\nvariable brane tension. Our investigation shows that the variable brane tension\nstrongly affects the shape and evolution of the black string horizon along the\nextra dimension, at least in a near-brane expansion. In particular, we apply\nour general analysis to a model motivated by the E\\"otv\\"os branes, where the\nvariable brane tension is related to the Friedmann-Robertson-Walker brane-world\ncosmology. We show that for some stages in the evolution of the universe, the\nblack string warped horizon collapses to a point and the black string has\ncorrespondingly finite extent along the extra dimension. Furthermore, we show\nthat in the minimal geometric deformation of a black hole on the variable\ntension brane, the black string has a throat along the extra dimension, whose\narea tends to zero as time goes to infinity.\n