A new exact solution of black-strings-like with a dS core

Abstract

We provide a new five dimensional black string-like solution by means of the embedding of a four dimensional regular black hole into a compact extra dimension. We enunciate a list of constraints in order to that the five dimensional black string-like solution to be regular, and, following these constraints we construct our solution. Instead of the usual singularity, it is formed a core whose topology corresponds to the product between the de-Sitter core of the four dimensional Hayward solution and S 1 . The horizon has topology S 2 × S 1 . At infinity of the radial coordinate the regular four dimensional geometry is asymptotically flat, i.e, at this place the topology of the complete solution corresponds to the product between Minkowski and S 1 . At the induced four dimensional geometry we compute the correct values of temperature and entropy.

Regular Schwarzschild-like spacetime embedded in a five dimensional bulk

“…where b ′ = db/dz and ρ, p r , p θ , p φ , p z are, respectively, the energy density, radial pressure and transversal pressures. To simplify his system of differential equations, Estrada [24] assumed that the scale factor b(z)(A(z) in his notations) has a constant derivative b ′ = db/dz (related with his cosmological constant) and so he obtained b ′′ (z) = 0. We choose a different option and take…”

“…There is no any horizon on the bulk but only that one on the brane, calculated from f (r) = 0 1 . As in Maartens [11] example, our BS has a cylindrical shape in the z-direction (see also [24]) but it is a sphere on the brane, with the bulk horizon radius obtained from g tt = 0.…”

“…Motivated by Estrada's paper, we make use of a different regular Schwarzschildtype metric [26,27] with an exponential factor that makes finite all physical quantities (including invariants) at the origin and at infinity. In addition, our constraint equation of the conformal factor of the 4-dimensional line-element on the brane is different from that used by Estrada [24], such that the conformal factor is an even function of the fifth dimension. Section 2 presents the 5-dimensional geometry in terms of a conformal factor b(z) in front of a regular Schwarzschild-like metric.…”

“…More recently, Estrada [24] provides a new five dimensional solution by em-bedding a four dimensional regular BH (the Hayward metric) into a compact extra dimension, with an asymptotically flat four dimensional geometry at infinity of the radial coordinate and a de Sitter core instead of a central singularity.…”

Representation of compact stars using the black string set-up

“…Recently, a new methodology has been provided for the representation of a 4-dimensional regular black hole into an extra dimension using the black string framework [13]. An inter-FIG.…”