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Jebsen-Birkhoff theorem and its stability in f(R) gravity
General Relativity and Quantum Cosmology · Submitted 24 Dec 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity in order to to find the necessary conditions required for the existence of the Schwarzschild solution in these theories and demonstrate that the rigidity of such solutions of f(R) gravity is valid even in the perturbed scenario.
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The abstract, sentence by sentence
We prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity in order to to find the necessary conditions required for the existence of the Schwarzschild solution in these theories and demonstrate that the rigidity of such solutions of f(R) gravity is valid even in the perturbed scenario.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity in order to to find the necessary conditions required for the existence of the Schwarzschild solution in these theories and demonstrate that the rigidity of such solutions of f(R) gravity is valid even in the perturbed scenario. | contribution 0.96 | 0.95 | 0.88 | asserted 1.00 |
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The paper
Original abstract
We prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity in order to to find the necessary conditions required for the existence of the Schwarzschild solution in these theories and demonstrate that the rigidity of such solutions of f(R) gravity is valid even in the perturbed scenario.
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References
How the literature uses it
11 arXiv papers cite this in 15 sentences
Papers citing it · 9 sentences without a confident label
Cites it as support 1 paper
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Even in the case of $f(R)$ gravity, the conditions on validity and stability of the Jebsen-Birkhoff theorem, ensure that the solution will remain “almost" Schwarzschild in the exterior domain for Starobinsky model provided the value of $α$ is small [ref] .
Neutron stars in Starobinsky model · Conclusion · 0.98
Cites it as background 5 papers
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Weaker version of the Birkhoff theorem have been discussed in the context of $f(R)$-theory [ref] , scalar tensor theory [ref] and $f(𝕋)$-gravity [ref] , and further modified theories of gravity [ref] .
Static spherically symmetric black holes in weak f(T)-gravity · Introduction · 0.89
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The existence and stability conditions for both Minkowski and Schwarzschild spacetimes in the context of $f(R)$ gravity have been studied by several authors, see [ref] .
Characteristic Formulation for Metric $f(R)$ Gravity · Introduction · 0.95
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([ref]), contains indeed 4-th order derivatives of the metric, analogously to what happens for the equations of motion (an account of Birkhoff-like theorems in $f(R)$ theories can be found in [ref] ; an investigation of the conditions which theories with equations of motion of order larger than 2 in the derivatives of the metric should obey for Birkhoff-like theorem to hold, is in [ref] ).
Null-null components of the generalized Einstein tensor for Lovelock models · Comments and conclusions · 0.87
What it cites · 15 sentences without a confident label
Uses the method or tool of 5 papers
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We prove the result by using the 1+1+2 covariant perturbation formalism [ref] , which developed from the 1+3 covariant perturbation formalism [ref] .
Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes · Introduction · 0.99
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We prove the result by using the 1+1+2 covariant perturbation formalism [ref] , which developed from the 1+3 covariant perturbation formalism [ref] .
A covariant approach for perturbations of rotationally symmetric spacetimes · Introduction · 0.99
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We prove the result by using the 1+1+2 covariant perturbation formalism [ref] , which developed from the 1+3 covariant perturbation formalism [ref] .
Covariant Perturbations of Schwarzschild Black Holes · Introduction · 0.99
Cites as background 2 papers
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A spacetime is said to be locally rotationally symmetric (LRS) if there exists a continuous isotropy group at each point and hence is characterised by the existence of a multi-transitive isometry group acting on the spacetime manifold [ref] .
Invariant construction of solutions to Einstein's field equations - LRS perfect fluids II · 1+1+2 equations for vacuum LRS-II spacetimes · 0.96
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A spacetime is said to be locally rotationally symmetric (LRS) if there exists a continuous isotropy group at each point and hence is characterised by the existence of a multi-transitive isometry group acting on the spacetime manifold [ref] .
The Covariant Approach to LRS Perfect Fluid Spacetime Geometries · 1+1+2 equations for vacuum LRS-II spacetimes · 0.96
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