标题： 星体配置在f(R)引力理论中 显示英文标题

标题： Stellar configurations in f(R) theories of gravity

摘要： 我们研究度规$f(R)$引力理论中的恒星结构及其周围的时空。 特别是，我们关注太阳的多态模型在$f(R)=R-\mu^4/R$模型中的情况。 我们展示了在$f(R)$理论中，通过适当的初始条件，恒星结构可以选择为与 Lane-Emden 方程描述的结构相同，并且解之间存在简单的缩放关系。 我们还分析地推导了在$f(R)$理论中恒星中心附近的正确解。 之前的分析和数值结果得到了确认，表明太阳周围的时空与太阳系对引力特性的约束不相容。 数值工作显示，具有中心正则度规的恒星结构会在恒星外部导致$\gamma_{PPN}\simeq1/2$，即施瓦茨希尔德-德西特时空不是此类结构的正确真空解。 相反，通过选择施瓦茨希尔德-德西特度规作为外部解，我们发现恒星结构不变，但度规在中心是不规则的。 讨论了构建与太阳系实验相容的$f(R)$理论的可能性，以及由恒星物体的半径-质量关系产生的可能新约束。 显示英文摘要

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 $f(R)=R-\mu^4/R$ 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 $\gamma_{PPN}\simeq1/2$ 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.