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Quest for Localized 4-D Black Holes in Brane Worlds
High Energy Physics - Theory · Submitted 31 Oct 2001
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It turns out that an exotic, shell-like distribution of matter is required.
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The abstract, sentence by sentence
We investigate the possibility of obtaining localized black hole solutions in brane worlds by introducing a dependence of the four-dimensional line--element on the extra dimension. An analysis, performed for the cases of an empty bulk and of a bulk containing either a scalar or a gauge field, reveals that no conventional type of matter can support such a dependence. Considering a particular ansatz for the five-dimensional line--element that corresponds to a black hole solution with a ``decaying'' horizon, we determine the bulk energy--momentum tensor capable of sustaining such a behaviour. It turns out that an exotic, shell-like distribution of matter is required. For such solutions, the black hole singularity is indeed localized near the brane and the spacetime is well defined near the AdS horizon, in contrast to the behaviour found in black string type solutions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the possibility of obtaining localized black hole solutions in brane worlds by introducing a dependence of the four-dimensional line--element on the extra dimension. | contribution 0.98 | 0.88 | 0.07 | hedged possibility 0.94 |
| s1 | An analysis, performed for the cases of an empty bulk and of a bulk containing either a scalar or a gauge field, reveals that no conventional type of matter can support such a dependence. | result 0.98 | 0.92 | 0.33 | asserted 1.00 |
| s2 | Considering a particular ansatz for the five-dimensional line--element that corresponds to a black hole solution with a ``decaying'' horizon, we determine the bulk energy--momentum tensor capable of sustaining such a behaviour. | method 0.71 | 0.94 | 0.10 | asserted 1.00 |
| s3 | It turns out that an exotic, shell-like distribution of matter is required. | result 0.99 | 0.92 | 0.37 | asserted 1.00 |
| s4 | For such solutions, the black hole singularity is indeed localized near the brane and the spacetime is well defined near the AdS horizon, in contrast to the behaviour found in black string type solutions. | result 0.88 | 0.88 | 0.45 | asserted 1.00 |
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The paper
Original abstract
We investigate the possibility of obtaining localized black hole solutions in brane worlds by introducing a dependence of the four-dimensional line--element on the extra dimension. An analysis, performed for the cases of an empty bulk and of a bulk containing either a scalar or a gauge field, reveals that no conventional type of matter can support such a dependence. Considering a particular ansatz for the five-dimensional line--element that corresponds to a black hole solution with a ``decaying'' horizon, we determine the bulk energy--momentum tensor capable of sustaining such a behaviour. It turns out that an exotic, shell-like distribution of matter is required. For such solutions, the black hole singularity is indeed localized near the brane and the spacetime is well defined near the AdS horizon, in contrast to the behaviour found in black string type solutions.
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References
How the literature uses it
22 arXiv papers cite this in 34 sentences
Papers citing it · 19 sentences without a confident label
Builds on it 2 papers
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In an effort to derive the long-sought analytical black-hole solutions, in [ref] the previously proposed idea [ref] , of adding a non-trivial profile along the extra dimension to the black-hole mass function in the original line element used in [ref] , 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-Nordström type] and to allow also for non-static configurations.
Five-dimensional gravitational brane-world models: Solutions for black strings and black holes · Introduction · 0.81
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In an effort to derive the long-sought analytical black-hole solutions, in [ref] the previously proposed idea [ref] , of adding a nontrivial profile along the extra dimension to the black-hole mass function in the original line element used in [ref] , 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.
Anti-Gravitating Brane-World Solutions for a de Sitter Brane in Scalar-Tensor Gravity · Introduction · 0.83
Compares with it 2 papers
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Employing the inverse transformations ([ref]), the line-element takes the form $ds^2 =e^-2k|y|{-f(r,y) dt^2+dr^2/r^2+z^2(y)[r^2/f(r,y)+z^2(y)]. +r^2dΩ_2^2+.2r z(y) e^k|y|/r^2+z^2(y)[1/f(r,y)-1]drdy } +dy^2/r^2+z^2(y)[r^2+z^2(y)/f(r,y)] ,$ where $z=sgn(y) (e^k |y|-1)/k$ and $f(r,y)=1-2M/√(r^2+z^2(y)) .$ We observe that the aforementioned line-element differs significantly from the factorised line-element employed in [ref] , or from non-factorised ones which appeared in a number of subsequent works [ref] .
Localized brane-world black hole analytically connected to an AdS$_5$ boundary · THE GEOMETRY · 0.94
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Employing the inverse transformations ([ref]), the line-element takes the form $ds^2=e^-2k|y| {-f(r,y) dt^2+dr^2/r^2+z^2(y)[r^2/f(r,y)+z^2(y)]+r^2dΩ_2^2 +2r z(y) e^k|y|/r^2+z^2(y)[1/f(r,y)-1]drdy } +dy^2/r^2+z^2(y)[r^2+z^2(y)/f(r,y)] ,$ where $z=sgn(y) (e^k |y|-1)/k$ and $f(r,y)=1-2M/√(r^2+z^2(y)) .$ We observe that the aforementioned line-element differs significantly from the factorized line-element employed in [ref] , or from non-factorized ones which appeared in a number of subsequent works [ref] .
Five-dimensional gravitational brane-world models: Solutions for black strings and black holes · Introduction · 1.00
Cites it as background 10 papers
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There is a plethora of attempts in the literature that try to derive a 5-dimensional black hole which is localized close to the brane (we mention some of them: [ref] .
Searching for Localized Black-Hole solutions in Brane-World models · Kaluza-Klein Modes · 0.99
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Our action is determined by [equation] where \(α\) is a dimensionless constant and where $L_B$ is the bulk lagrangian [ref] .
A way of decoupling the gravitational bulk field equations of regular braneworld black holes to suppress the bulk singularities · Action and equations of motion · 0.80
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Furthermore, although some studies have attempted to identify the underlying field theories capable of supporting such geometries [ref] , providing a complete and consistent field-theoretic description remains a challenging task.
Embedding Wormholes and Dyonic Black Strings in Warped Braneworlds via Local Sum Rules · Introduction · 0.80
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