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arXiv 0709.0891gr-qcastro-ph
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$f(R)$ -引力中的球对称性

Spherical symmetry in $f(R)$-gravity

S. Capozziello, A. Stabile, A. Troisi

摘要:

本文详细讨论了$f(R)$引力场的球对称性,并考虑了球对称性与弱场极限的关系。对于常Ricci曲率标量和依赖于径向坐标的Ricci标量,得到了精确解。特别是,我们讨论了如何获得可以与给出众所周知的后牛顿和后闵可夫斯基极限的广义相对论一致比较的结果。此外,我们实现了一个扰动的方法来获得解决方案,从球对称背景的第一顺序。给出了几类$f(R)$理论在$R =$常数和$R = R(r)$下的精确解.

英文摘要:

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 $R = R(r)$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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