New black-string solutions for an anti-de Sitter brane in scalar-tensor gravity

We consider a five-dimensional theory with a scalar field nonminimally coupled to gravity, and we look for novel black-string solutions in the bulk. By appropriately choosing the nonminimal coupling function of the scalar field, we analytically solve the gravitational and scalar-field equations in the bulk to produce black-string solutions that describe a Schwarzschild-anti-de Sitter space-time on the brane. We produce two complete such solutions that are both characterized by a regular scalar field, a localized-close-to-our-brane energy-momentum tensor and a negative-defmite, nontrivial bulk potential that may support by itself the warping of the space-time even in the absence of the traditional, negative, bulk cosmological constant. Despite the infinitely long string singularity in the bulk, the four-dimensional effective theory on the brane is robust, with the effective gravity scale being related to the fundamental one and the warping scale. It is worth noting that if we set the mass of the black hole on the brane equal to 0, the black string disappears, leaving behind a regular brane-world model with only a true singularity at the boundary of the fifth dimension.