标题： 高曲率引力中的非相对论性恒星结构：修正的Lane-Emden方程解的系统构造 显示英文标题

标题： Non-relativistic stellar structure in higher-curvature gravity: systematic construction of solutions to the modified Lane-Emden equations

摘要： 我们研究了由非相对论性多态流体组成的静态球对称星体在高曲率引力理论（HCG）线性化框架下的结构。首先，我们以规范不变的方式推导出恒星分布函数的修正Lane-Emden（LE）方程，在一般情况下该方程归结为六阶微分方程，而在两种特殊情形下则退化为四阶方程，这反映了每种理论中额外出现的质量引力子的数量。此外，质量引力子的存在使边界值问题的性质不同于标准的LE方程：一些边界条件不能再仅通过恒星中心的物理条件来表述，而恒星表面的一些要求必然需要考虑。我们提出了一种实用的方法来构建此类问题的解，并演示了它在多态指数n=0和1的情况下的工作原理，其中修正的LE方程存在解析解。作为物理结果，我们阐明了恒星半径、质量以及Yukawa电荷如何依赖于理论参数，以及这些可观测量之间的相互关系。得到了合理的Weyl平方校正的上限。 显示英文摘要

摘要： We study the structure of static spherical stars made up of a non-relativistic polytropic fluid in linearized higher-curvature theories of gravity (HCG). We first formulate the modified Lane-Emden (LE) equation for the stellar profile function in a gauge-invariant manner, finding it boils down to a sixth order differential equation in the generic case of HCG, while it reduces to a fourth order equation in two special cases, reflecting the number of additional massive gravitons arising in each theory. Moreover, the existence of massive gravitons renders the nature of the boundary-value problem unlike the standard LE: some of the boundary conditions can no longer be formulated in terms of physical conditions at the stellar center alone, but some demands at the stellar surface necessarily come into play. We present a practical scheme for constructing solutions to such a problem and demonstrate how it works in the cases of the polytropic index n = 0 and 1, where analytical solutions to the modified LE equations exist. As physical outcomes, we clarify how the stellar radius, mass, and Yukawa charges depend on the theory parameters and how these observables are mutually related. Reasonable upper bounds on the Weyl-squared correction are obtained.