A note on constant curvature solutions in cylindrically symmetric metric $f(R)$ Gravity

Details A note on constant curvature solutions in cylindrically symmetric metric $f(R)$ Gravity A note on constant curvature solutions in cylindrically symmetric metric $f(R)$ Gravity

2009-02-28

arxiv.org/abs/0903.0067v7

Int.J.Mod.Phys.D18:1719-1729,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages,Typos corrected and references added, accepted for publication in "International journal of modern physics D"(IJMPD),

Scientific paper

10.1142/S0218271809015266

In the previous work we introduced a new static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity\cite{1}. Now we obtain a 2-parameter family of exact solutions which contains cosmological constant and a new parameter as $\beta$. This solution corresponds to a constant Ricci scalar. We proved that in $f(R)$ gravity, the constant curvature solution in cylindrically symmetric cases is only one member of the most generalized Tian family in GR. We show that our constant curvature exact solution is applicable to the exterior of a string. Sensibility of stability under initial conditions is discussed.

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