Spherical symmetry in <i>f</i> ( <i>R</i> )-gravity
S CapozzielloDipartimento di Scienze Fisiche and INFN, Sez di Napoli, Università di Napoli ‘Federico II’, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 - Napoli, ItalyA StabileDipartimento di Fisica ‘E R Caianiello’, Università degli Studi di Salerno, Via S Allende, I-84081 Baronissi (SA), ItalyA TroisiDipartimento di Scienze Fisiche and INFN, Sez di Napoli, Università di Napoli ‘Federico II’, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 - Napoli, Italy
2008en
ABI
Abstract
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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Cited by 30 references