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Exact and asymptotic black branes with spherical compactification
General Relativity and Quantum Cosmology · Submitted 13 Feb 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity.
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The abstract, sentence by sentence
In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant $\Lambda_6$, we obtain the black brane with spherical compactification of the internal space. The matter source for this exact solution consists of two parts. First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension $\hat p_1=-(1/2)\hat\varepsilon$ in the internal space. This solution exists both in the presence and absence of $\Lambda_6$. In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state $\hat p_1=\Omega \hat\varepsilon$ in the internal space. In the case $\Lambda_6>0$ and $\Omega\neq -1/2$, these approximate solutions tend asymptotically to the weak-field limit of the exact black brane solution. Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant $\Lambda_6$, we obtain the black brane with spherical compactification of the internal space. | contribution 0.69 | 0.93 | 0.43 | asserted 1.00 |
| s1 | The matter source for this exact solution consists of two parts. | result 0.51 | 0.68 | 0.04 | asserted 1.00 |
| s2 | First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. | result 0.57 | 0.80 | 0.08 | asserted 1.00 |
| s3 | Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension $\hat p_1=-(1/2)\hat\varepsilon$ in the internal space. | result 0.56 | 0.84 | 0.07 | asserted 1.00 |
| s4 | This solution exists both in the presence and absence of $\Lambda_6$. | result 1.00 | 0.85 | 0.12 | asserted 1.00 |
| s5 | In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. | contribution 0.51 | 0.93 | 0.06 | asserted 1.00 |
| s6 | Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state $\hat p_1=\Omega \hat\varepsilon$ in the internal space. | result 0.75 | 0.91 | 0.05 | asserted 1.00 |
| s7 | In the case $\Lambda_6>0$ and $\Omega\neq -1/2$, these approximate solutions tend asymptotically to the weak-field limit of the exact black brane solution. | result 0.98 | 0.88 | 0.12 | asserted 1.00 |
| s8 | Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity. | result 0.72 | 0.77 | 0.41 | asserted 1.00 |
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Original abstract
In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant $\Lambda_6$, we obtain the black brane with spherical compactification of the internal space. The matter source for this exact solution consists of two parts. First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension $\hat p_1=-(1/2)\hat\varepsilon$ in the internal space. This solution exists both in the presence and absence of $\Lambda_6$. In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state $\hat p_1=\Omega \hat\varepsilon$ in the internal space. In the case $\Lambda_6>0$ and $\Omega\neq -1/2$, these approximate solutions tend asymptotically to the weak-field limit of the exact black brane solution. Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity.
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How the literature uses it
2 arXiv papers cite this in 13 sentences
Papers citing it · 6 sentences without a confident label
Builds on it 1 paper
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For completeness, we also generalize the linear model $f(R)=R+2κΛ_6$ previously considered in [ref] to the case of an arbitrary nonlinear background perfect fluid.
Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification · Introduction · 0.99
Compares with it 1 paper
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We note here that in the linear model with $f”(R_0)= 0$, 1.25 is reduced to its counterpart obtained in papers [ref] .
Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification · Basic equations · 0.98
What it cites · 3 sentences without a confident label
Uses data or values from 1 paper
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If, for example, $|Ω| ∼O(1)$ (and is not equal to -1/2), the upper limit for $λ$ is $λ_ ∼10^-3$cm [ref] .
Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale · Asymptotic black brane · 0.82
Cites as background 4 papers
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For black strings and black branes, the notion of tension is defined, e.g., in [ref] and it follows from the first law for black hole spacetimes [ref] .
Tension Perturbations of Black Brane Spacetimes · Introduction · 0.93
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For black strings and black branes, the notion of tension is defined, e.g., in [ref] and it follows from the first law for black hole spacetimes [ref] .
The first law of black brane mechanics · Introduction · 0.93
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For black strings and black branes, the notion of tension is defined, e.g., in [ref] and it follows from the first law for black hole spacetimes [ref] .
General Definition of Gravitational Tension · Introduction · 0.93
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