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In the framework of a general scalar-tensor theory, where the scalar field isnon-minimally coupled to the five-dimensional Ricci scalar curvature, weinvestigate the emergence of complete brane-world solutions. By assuming avariety of forms for the coupling function, we solve the field equations in thebulk, and determine in an analytic way the form of the gravitational backgroundand scalar field in each case. The solutions are always characterized by aregular scalar field, a finite energy-momentum tensor, and an exponentiallydecaying warp factor even in the absence of a negative bulk cosmologicalconstant. The space-time on the brane is described by the Schwarzschildsolution leading to either a non-homogeneous black-string solution in the bulk,when the mass parameter $M$ is non-zero, or a regular anti-de Sitterspace-time, when $M=0$. We construct physically-acceptable solutions bydemanding in addition a positive effective gravitational constant on our brane,a positive total energy-density for our brane and the validity of the weakenergy condition in the bulk. We find that, although the theory does not allowfor all three conditions to be simultaneously satisfied, a plethora ofsolutions emerge which satisfy the first two, and most fundamental, conditions.

Incorporating Physical Constraints in Braneworld Black-String Solutions for a Minkowski Brane in Scalar-Tensor Gravity