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Anisotropic fluid from nonlocal tidal effects
General Relativity and Quantum Cosmology · Submitted 15 Feb 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The non-local tensor $E_{ab}$ generated by the 5-dimensional Weyl tensor gives rise at an anisotropic energy-momentum tensor on the brane with negative energy density and $p = \rho/3$ as equation of state.
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The abstract, sentence by sentence
The Shiromizu et al. \cite{SMS} covariant decomposition formalism is used to find out the brane properties rooted from the 5-dimensional Witten bubble spacetime. The non-local tensor $E_{ab}$ generated by the 5-dimensional Weyl tensor gives rise at an anisotropic energy-momentum tensor on the brane with negative energy density and $p = \rho/3$ as equation of state. The tidal acceleration is towards the brane and that is in accordance with the negative energy density on the brane. The anisotropic fluid has vanishing "bulk" viscosity but the shear viscosity coefficient is $r$- and $t$- dependent. The brane is endowed with an apparent horizon which is exactly the radial null geodesic.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Shiromizu et al. \cite{SMS} covariant decomposition formalism is used to find out the brane properties rooted from the 5-dimensional Witten bubble spacetime. | method 0.94 | 0.60 | 0.06 | asserted 1.00 |
| s1 | The non-local tensor $E_{ab}$ generated by the 5-dimensional Weyl tensor gives rise at an anisotropic energy-momentum tensor on the brane with negative energy density and $p = \rho/3$ as equation of state. | result 0.99 | 0.70 | 0.68 | asserted 1.00 |
| s2 | The tidal acceleration is towards the brane and that is in accordance with the negative energy density on the brane. | interpretation 0.70 | 0.71 | 0.16 | asserted 0.96 |
| s3 | The anisotropic fluid has vanishing "bulk" viscosity but the shear viscosity coefficient is $r$- and $t$- dependent. | result 1.00 | 0.81 | 0.12 | asserted 1.00 |
| s4 | The brane is endowed with an apparent horizon which is exactly the radial null geodesic. | result 1.00 | 0.77 | 0.12 | asserted 1.00 |
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The paper
Original abstract
The Shiromizu et al. \cite{SMS} covariant decomposition formalism is used to find out the brane properties rooted from the 5-dimensional Witten bubble spacetime. The non-local tensor $E_{ab}$ generated by the 5-dimensional Weyl tensor gives rise at an anisotropic energy-momentum tensor on the brane with negative energy density and $p = \rho/3$ as equation of state. The tidal acceleration is towards the brane and that is in accordance with the negative energy density on the brane. The anisotropic fluid has vanishing "bulk" viscosity but the shear viscosity coefficient is $r$- and $t$- dependent. The brane is endowed with an apparent horizon which is exactly the radial null geodesic.
Human review
How the literature uses it
2 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
Uses its method or tool 1 paper
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Shiromizu et al. [ref] (see also [ref] ) have shown that, from the Gauss equations relating the Riemann tensors in 5- and 4-dimensions and the Codazzi equations for the variation of the extrinsic curvature, one readily obtains [equation] where $^5R_ab$ is the 5-dimensional Ricci tensor, $K = K^a_ a$ is the trace of the extrinsic curvature $K_ab = h^c_ah^d_b∇_cn_d$ and [equation] is the tensor related to the tidal effects on the brane, coming from the bulk.
Regular Schwarzschild-like spacetime embedded in a five dimensional bulk · The anisotropic stress tensor · 0.90
Cites it as background 1 paper
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In the brane-world scenario, one considers that the standard matter fields are confined to the 4-dimensional spacetime (the brane) whereas gravity propagates in the full spacetime (the bulk) [ref] .
Regular Schwarzschild-like spacetime embedded in a five dimensional bulk · Introduction · 0.98
What it cites · 16 sentences without a confident label
Uses the method or tool of 1 paper
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By means of the covariant decomposition developed by Shiromizu et al. [ref] we write down the effective gravitational equations on the brane.
The Einstein Equations on the 3-Brane World · Introduction · 1.00
Compares with 4 papers
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But $G_5$ is usually taken as $LG_4$, so (3.6) is obtained ($G_4$ is the Newton constant in 4 dimensions).] [equation] The brane geometry (the dimensionally reduced Witten bubble) is obtained taking $y = 0$ in (2.2) [equation] We obtained previously [ref] (see also [ref] ) the same $T^a_ b$ but with (3.7) written in its conformally-flat form.
Kinematic quantities for a spherical distribution of uniformly accelerated observers · Brane-world stress tensor · 0.88
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But $G_5$ is usually taken as $LG_4$, so (3.6) is obtained ($G_4$ is the Newton constant in 4 dimensions).] [equation] The brane geometry (the dimensionally reduced Witten bubble) is obtained taking $y = 0$ in (2.2) [equation] We obtained previously [ref] (see also [ref] ) the same $T^a_ b$ but with (3.7) written in its conformally-flat form.
Boundary stress tensors for spherically symmetric conformal Rindler observers · Brane-world stress tensor · 0.88
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But $G_5$ is usually taken as $LG_4$, so (3.6) is obtained ($G_4$ is the Newton constant in 4 dimensions).] [equation] The brane geometry (the dimensionally reduced Witten bubble) is obtained taking $y = 0$ in (2.2) [equation] We obtained previously [ref] (see also [ref] ) the same $T^a_ b$ but with (3.7) written in its conformally-flat form.
Semiclassical instability of the brane-world: Randall-Sundrum bubbles · Brane-world stress tensor · 0.88
Cites as background 8 papers
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In the brane-world scenario, standard matter fields are confined to the 4-dimensional spacetime (the brane) whereas gravity propagates in the full spacetime (the bulk) [ref] .
The Einstein Equations on the 3-Brane World · Introduction · 0.99
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In the brane-world scenario, standard matter fields are confined to the 4-dimensional spacetime (the brane) whereas gravity propagates in the full spacetime (the bulk) [ref] .
Gravity, Stability and Energy Conservation on the Randall-Sundrum Brane-World · Introduction · 0.99
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Gravity becomes a truly higher dimensional theory at short ranges, when string theory/M theory applies [ref] .
Geometry and dynamics of the brane-world · Introduction · 0.96
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