f（R）引力理论中的恒星构形
Stellar configurations in f(R) theories of gravity
摘要：
我们研究恒星的配置和周围的时空在度规$f(R)$引力理论。特别是，我们专注于太阳的多方模型中的$f(R)=R-μ^4/R$模型。我们展示了如何恒星配置的$f(R)$理论可以，通过适当的初始条件，被选择为等于所描述的Lane-Emden方程和如何一个简单的标度关系之间存在的解决方案。我们还推导出正确的解决方案解析附近的恒星中心的$f(R)$理论。以前的分析和数值计算结果得到证实，表明太阳周围的时空是不相容的太阳系的引力性质的限制。数值计算表明，恒星的配置，与一个定期度规在中心，导致$γ_{PPN}\simeq1/2$以外的恒星即。Schwarzschild-de Sitter时空不是这种构型的正确真空解。相反，通过选择Schwarzschild-de Sitter度规作为外部解，我们发现恒星的构型不变，但度规在中心是不规则的。本文讨论了建立一个与太阳系实验相兼容的$f(R)$理论的可能性以及由天体半径-质量关系引起的可能的新约束。
英文摘要：
We study stellar configurations and the space-time around them in metric $f(R)$ theories of gravity. In particular, we focus on the polytropic model of the Sun in the $f(R)=R-μ^4/R$ model. We show how the stellar configuration in the $f(R)$ theory can, by appropriate initial conditions, be selected to be equal to that described by the Lane-Emden -equation and how a simple scaling relation exists between the solutions. We also derive the correct solution analytically near the center of the star in $f(R)$ theory. Previous analytical and numerical results are confirmed, indicating that the space-time around the Sun is incompatible with Solar System constraints on the properties of gravity. Numerical work shows that stellar configurations, with a regular metric at the center, lead to $γ_{PPN}\simeq1/2$ outside the star ie. the Schwarzschild-de Sitter -space-time is not the correct vacuum solution for such configurations. Conversely, by selecting the Schwarzschild-de Sitter -metric as the outside solution, we find that the stellar configuration is unchanged but the metric is irregular at the center. The possibility of constructing a $f(R)$ theory compatible with the Solar System experiments and possible new constraints arising from the radius-mass -relation of stellar objects is discussed.
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