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Brane-$f(R)$ gravity and dark matter
General Relativity and Quantum Cosmology · Submitted 22 Feb 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations and contributes to gravitational energy and that such a geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies.
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The abstract, sentence by sentence
The collision-free Boltzmann equation is used in the context of brane-$f(R)$ gravity to derive the virial theorem. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations and contributes to gravitational energy and that such a geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. In addition, the galaxy rotation curves are studied by utilizing the concept of conformal symmetry and notion of conformal Killing symmetry. The field equations may then be obtained in an exact parametric form in terms of the parameter representing the conformal factor. This provides the possibility of studying the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity can be derived as a function of the conformal factor and integration constants, resulting in a constant value at large radial distances. Relevant phenomenon such as the deflection of light passing through a region where the rotation curves are flat and the radar echo delay are also studied.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The collision-free Boltzmann equation is used in the context of brane-$f(R)$ gravity to derive the virial theorem. | method 0.93 | 0.84 | 0.06 | asserted 1.00 |
| s1 | It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations and contributes to gravitational energy and that such a geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. | result 0.80 | 0.88 | 0.64 | asserted 0.99 |
| s2 | In addition, the galaxy rotation curves are studied by utilizing the concept of conformal symmetry and notion of conformal Killing symmetry. | contribution 0.51 | 0.82 | 0.05 | asserted 0.97 |
| s3 | The field equations may then be obtained in an exact parametric form in terms of the parameter representing the conformal factor. | method 0.52 | 0.79 | 0.05 | hedged possibility 0.98 |
| s4 | This provides the possibility of studying the behavior of the angular velocity of a test particle moving in a stable circular orbit. | contribution 0.49 | 0.55 | 0.04 | hedged possibility 0.95 |
| s5 | The tangential velocity can be derived as a function of the conformal factor and integration constants, resulting in a constant value at large radial distances. | result 1.00 | 0.86 | 0.16 | asserted 1.00 |
| s6 | Relevant phenomenon such as the deflection of light passing through a region where the rotation curves are flat and the radar echo delay are also studied. | contribution 0.98 | 0.80 | 0.06 | asserted 0.98 |
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The paper
Original abstract
The collision-free Boltzmann equation is used in the context of brane-$f(R)$ gravity to derive the virial theorem. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations and contributes to gravitational energy and that such a geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. In addition, the galaxy rotation curves are studied by utilizing the concept of conformal symmetry and notion of conformal Killing symmetry. The field equations may then be obtained in an exact parametric form in terms of the parameter representing the conformal factor. This provides the possibility of studying the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity can be derived as a function of the conformal factor and integration constants, resulting in a constant value at large radial distances. Relevant phenomenon such as the deflection of light passing through a region where the rotation curves are flat and the radar echo delay are also studied.
Human review
How the literature uses it
1 arXiv paper cite this in 2 sentences
Papers whose main result relates to this one's
States the same result 2 papers
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The extra terms in the modified Einstein equations generate an equivalent mass term (geometrical mass), which give an effective contribution to the gravitational energy and offer viable explanation to account for the virial mass discrepancy in clusters of galaxies.
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We show that the "geometrical mass" term may account for the well known virial mass discrepancy in clusters of galaxies.
What it cites · 27 sentences without a confident label
Uses the method or tool of 3 papers
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The effective Einstein field equations in the bulk can be written as [equation] where [equation] Using the SMS procedure [ref] , the field equations on the brane are given by [equation] We note that [equation] where $λ$ is the brane tension, $τ_μν$ is the energy momentum tensor on the brane and $π_μν$ is defined in terms of $τ_μν$ as [equation] The electric part of the Weyl tensor is given by [equation] where $n^A$ is the unit vector normal to the 4-dimensional brane and $h_AB=g_AB-n_An_B$ is the induced metric on the brane.
The Einstein Equations on the 3-Brane World · The brane-$f(R)$ gravity · 0.81
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In tetrad components, the relativistic Boltzmann equation can be written as [equation] where $f_B=f_B(x^μ,u^a)$ is the distribution function and $γ^a_b c=e^a_μ;νe^μ_b e^ν_c$ are the Ricci rotation coefficients [ref] .
Generalized virial theorem in f(R) gravity · The generalized virial theorem · 0.91
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This procedure also leads to the metric components in terms of the conformal factor [equation] and [equation] where $B$ and $C$ are integration constants [ref] .
Brane worlds and dark matter · Vacuum solution · 0.80
Cites as support 1 paper
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Therefore, one may conclude that Einsteins's gravity may break down at the scale of galaxies [ref] .
Can the galactic rotation curves be explained in brane world models? · Introduction · 0.97
Cites as background 14 papers
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The virial theorem has also been used in model $f(R)$ theories with a cosmological constant [ref] , within the context of brane-world scenarios [ref] , using both the metric [ref] and Palatini formalisms [ref] .
The virial theorem and the dynamics of clusters of galaxies in the brane world models · Introduction · 0.89
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The virial theorem has also been used in model $f(R)$ theories with a cosmological constant [ref] , within the context of brane-world scenarios [ref] , using both the metric [ref] and Palatini formalisms [ref] .
Generalized virial theorem in f(R) gravity · Introduction · 0.89
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The virial theorem has also been used in model $f(R)$ theories with a cosmological constant [ref] , within the context of brane-world scenarios [ref] , using both the metric [ref] and Palatini formalisms [ref] .
Generalized virial theorem in Palatini $f(R)$ gravity · Introduction · 0.89
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