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.
Highlights
The general theory of relativity [1–3] is a mathematically beautiful, tensorial theory of gravity that predicts a variety of fascinating gravitational objects such as black holes, wormholes or compact stars
This holds despite the fact that the value of λ does affect the exact, analytic expression of the scalar field, as we have shown in detail above; we may conclude that solutions emerging for nonminimal coupling functions of a simple exponential form, differing only in the value of the parameter λ, i.e., in the decrease rate of f with y, lead to a class of black-string solutions with the same qualitative characteristics
We have considered a five-dimensional gravitational theory containing a scalar field with a nonminimal coupling to the five-dimensional Ricci scalar
Summary
The general theory of relativity [1–3] is a mathematically beautiful, tensorial theory of gravity that predicts a variety of fascinating gravitational objects such as black holes, wormholes or compact stars. The determination of regular black-hole solutions in the context of the so-called brane-world models [11,12] has been a challenging task that, in part, remains still unfulfilled These models present the additional complication of the presence of the self-energy of the brane, which is one of the fundamental features of the theory as it gives rise to the desired warping of space-time. In [34,41], the same theory was exhaustively studied for the determination of an analytical solution describing a regular black hole localized close to our brane; apart from the scalar degree of freedom (d.o.f.) that was supplemented by an arbitrary bulk potential, a generalized ansatz for the higher-dimensional line element was employed that allowed for a diverse, and even dynamical, black-hole solution on the brane.
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