Abstract
In the framework of a general scalar-tensor theory, where the scalar field is non-minimally coupled to the five-dimensional Ricci scalar curvature, we investigate the emergence of complete brane-world solutions. By assuming a variety of forms for the coupling function, we solve the field equations in the bulk, and determine in an analytic way the form of the gravitational background and scalar field in each case. The solutions are always characterized by a regular scalar field, a finite energy-momentum tensor, and an exponentially decaying warp factor even in the absence of a negative bulk cosmological constant. The space-time on the brane is described by the Schwarzschild solution 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 Sitter space-time, when $M=0$. We construct physically-acceptable solutions by demanding in addition a positive effective gravitational constant on our brane, a positive total energy-density for our brane and the validity of the weak energy condition in the bulk. We find that, although the theory does not allow for all three conditions to be simultaneously satisfied, a plethora of solutions emerge which satisfy the first two, and most fundamental, conditions.
Highlights
The first higher-dimensional formulation of the general theory of relativity [1,2,3] by Kaluza [4] and Klein [5] is almost as old as the original theory itself
In the framework of a general scalar-tensor theory, where the scalar field is nonminimally coupled to the five-dimensional Ricci scalar curvature, we investigate the emergence of complete braneworld solutions
In the context of this work, we have investigated the emergence of braneworld solutions in the framework of a general scalar-tensor theory where the scalar field is nonminimally coupled to the five-dimensional Ricci scalar
Summary
The first higher-dimensional formulation of the general theory of relativity [1,2,3] by Kaluza [4] and Klein [5] is almost as old as the original theory itself. The objective of the analyses in [31,38] was to derive an analytical solution describing a regular, localized black hole; no such solution was found, these studies hinted that black-string solutions were much easier to emerge in the context of a nonminimally coupled scalartensor braneworld model. Solving analytically the complete set of gravitational and scalar-field equations in the bulk, we determined novel black-string solutions which reduced to a Schwarzschild-(anti-)de Sitter space-time on the brane. In a follow-up work [73], we considered the case of a negative cosmological constant on the brane, which allowed positive-definite coupling functions; by employing two particular forms of the latter, we produced two complete analytical solutions that were characterized by a regular scalar field and a localized close-to-our brane energy-momentum tensor.
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