On the localisation of four-dimensional brane-world black holes: II. The general case

Abstract

We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the 5-dimensional metric tensor that allows for time-dependence, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions, energy-momentum tensor, solutions that have the form of a Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge, however, the resulting profile of the mass-function along the bulk coordinate, when allowed, is not the correct one to eliminate the bulk singularities.

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

“…Since then, and despite all efforts, no analytical, closed form of a regular, localised-on-the-brane black-hole solution has been found. During that quest, line-element (6) was used in a number of works [24,34,41] as it exhibited a second advantage: since it contained no horizon in its four-dimensional part, it did not lead to additional bulk singularities [20,24]. A generalized Vaidya form, where m is not a constant any more but a function of the coordinates, was employed in an effort to increase the flexibility of the model and allow for brane black-hole solutions to deviate from the overly simple Schwarzschild one.…”

Antigravitating braneworld solutions for a de Sitter brane in scalar-tensor gravity

“…Numerical solutions also emerged that described either small [44][45][46] or large black holes [47][48][49][50][51] in braneworld models. In an effort to derive the long-sought analytical blackhole solutions, in [52,53] the previously proposed idea [25], of adding a nontrivial profile along the extra dimension to the black-hole mass function in the original line element used in [13], was extended to include also a dependence on the time and radial coordinate; in this way, the rather restricted Schwarzschild-type of brane background was extended to include additional terms [of an (anti)-de Sitter or Reissner-Nordstrom type] and to allow also for nonstatic configurations. A large number of bulk scalar field theories were then investigated; however, no viable solutions that could sustain the line element of a five-dimensional, regular, localized-close-to-our-brane black hole was found.…”

“…We demonstrate that, for very natural, simple choices of the coupling function between the scalar field and the five-dimensional scalar curvature, novel black-string solutions may indeed be found with rather interesting and provocative characteristics. Given the fact that the same theory has resisted in giving legitimate black-hole solutions, even for a wider number of choices of the coupling function [52,53], our present results add new "fuel" to the long dispute around the question of why braneworld models lead quite easily to black-string solutions but not to localized black holes [54][55][56][57][58][59][60][61][62][63][64]. Indeed, higher-dimensional gravitational theories often allow for the emergence of uniform or nonuniform black-string solutions [65][66][67][68][69][70][71][72][73][74].…”

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

“…However, the five-dimensional scalar-tensor theory of gravity described by Eq. (2.1) was shown [31,38] to admit novel black-string solutions that may be constructed analytically. In our previous works [69,73], we performed a comprehensive study of the types of black-string solutions that emerge in the context of this theory when the cosmological constant on the brane is positive or negative, respectively.…”

“…Scalar-tensor theories of this type are very popular and have been extensively studied in the context of four-dimensional gravity, while brane-world generalizations have been studied in the literature before, both in static and non-static backgrounds [75][76][77][78][79][80]. The objective of the analyses in [31,38] was to derive an analytical solution describing a regular, localised black hole; although no such solution was found, these studies hinted that black-string solutions were in fact much easier to emerge in the context of a non-minimally coupled scalar-tensor brane-world model.…”