Spherical symmetry in $f(R)$-gravity

Details Spherical symmetry in $f(R)$-gravity Spherical symmetry in $f(R)$-gravity

2007-09-06

arxiv.org/abs/0709.0891v2

Class.Quant.Grav.25:085004,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages

Scientific paper

10.1088/0264-9381/25/8/085004

Spherical symmetry in $f(R)$ gravity is discussed in details considering also the relations with the weak field limit. Exact solutions are obtained for constant Ricci curvature scalar and for Ricci scalar depending on the radial coordinate. In particular, we discuss how to obtain results which can be consistently compared with General Relativity giving the well known post-Newtonian and post-Minkowskian limits. Furthermore, we implement a perturbation approach to obtain solutions up to the first order starting from spherically symmetric backgrounds. Exact solutions are given for several classes of $f(R)$ theories in both $R =$ constant and $R = R(r)$.

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