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

Abstract

We consider a five-dimensional theory with a scalar field non-minimally coupled to gravity, and we look for novel black-string solutions in the bulk. By appropriately choosing the non-minimal 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 characterised by a regular scalar field, a localised-close-to-our brane energy-momentum tensor and a negative-definite, non-trivial 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 zero, the black string disappears leaving behind a regular brane-world model with only a true singularity at the boundary of the fifth dimension. *

Incorporating physical constraints in braneworld black-string solutions for a Minkowski brane in scalar-tensor gravity

“…As in our previous works for positive [69] and negative cosmological constant [73] on the brane, it is clear that the parameter Λ appearing in the expression of the mass function (2.15), and in the projected-on-thebrane line-element (2.16) is indeed related to the four-dimensional cosmological constant Λ 4 . Therefore, in the context of the present analysis where we have set Λ = 0, we derived a vanishing Λ 4 as anticipated.…”

“…The latter is characterised by a self-interacting potential V B (Φ) and a non-minimal coupling to R via a coupling function f (Φ). As in our previous works [69,73], we will initially keep this function arbitrary so that our formalism is applicable to a large class of theories. In the above, κ 2 5 = 8πG 5 , where G 5 is the five-dimensional gravitational constant G 5 , and g (5) M N is the metric tensor of the five-dimensional space-time.…”

“…The form of the five-dimensional gravitational background needs to be specified next. As in [69,73], we consider the following line-element [11,12], in a black-string solution [14] with an infinitely-long singularity plagued by instabilities [54,55].…”

“…A solution for the scalar field similar to Eq. (5.6) was derived in the context of our previous analysis [73] for an exponential coupling function f (y) and an anti-de Sitter brane (Λ < 0). The mathematical properties of the solution were studied there in detail, therefore, here, we adapt those results in the present case and present our solutions for the scalar field without repeating the analysis-we refer the interested reader to our previous work for further information.…”

“…Having covered the cases of a de Sitter and anti-de Sitter space-time on our brane in [69,73], in this third instalment we turn our attention to the case of a Minkowski brane, i.e. with a vanishing effective cosmological constant.…”