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In the context of a five-dimensional theory with a scalar fieldnon-minimally-coupled to gravity, we look for solutions that describe novelblack-string or maximally-symmetric solutions in the bulk. The braneline-element is found to describe a Schwarzschild-(Anti)-de Sitter spacetime,and, here, we choose to study solutions with a positive four-dimensionalcosmological constant. We consider two different forms of the coupling functionof the scalar field to the bulk scalar curvature, a linear and a quadratic one.In the linear case, we find solutions where the theory, close to our brane,mimics an ordinary gravitational theory with a minimally-coupled scalar fieldgiving rise to an exponentially decreasing warp factor in the absence of anegative bulk cosmological constant. The solution is characterised by thepresence of a normal gravity regime around our brane and an anti-gravitatingregime away from it. In the quadratic case, there is no normal-gravity regimeat all, however, scalar field and energy-momentum tensor components arewell-defined and an exponentially decreasing warp factor emerges again. Wedemonstrate that, in the context of this theory, the emergence of a positivecosmological constant on our brane is always accompanied by an anti-gravitatingregime in the five-dimensional bulk.

Anti-Gravitating Brane-World Solutions for a de Sitter Brane in Scalar-Tensor Gravity