标题： 具有连续光盘的弯曲时空 显示英文标题

标题： Curved spacetimes with continuous light disks

摘要： 已知高度弯曲的致密天体时空具有光环（null圆型测地线），其半径为{\it 离散的}，在此半径上无质量粒子可以进行闭合圆周运动。 在目前这篇紧凑的论文中，我们首次揭示了存在具有光盘的各向同性弯曲时空，这些光盘由一系列闭合光环组成{\it 连续统}。 特别是，利用基于非线性耦合的爱因斯坦物质场方程的分析技术，我们证明了这些物理上有趣的时空包含一个半径为$r_->0$的中心致密核心，该核心支撑着一个外部球壳，壳中有无穷多个（连续的）null圆周测地线，所有这些测地线都由函数关系$4\pi r^2_{\gamma}p(r_{\gamma})=1-3m(r_{\gamma})/r_{\gamma}$和$8\pi r^2_{\gamma}(\rho+p)=1$描述，其中$r_{\gamma}\in[r_-,r_+]$表示 [这里$\{\rho,p\}$分别是自引力物质场的能量密度和各向同性压力，$m(r)$是半径为$r$的球面内包含的引力质量]。 显示英文摘要

摘要： Highly curved spacetimes of compact astrophysical objects are known to possess light rings (null circular geodesics) with {\it discrete} radii on which massless particles can perform closed circular motions. In the present compact paper, we reveal for the first time the existence of isotropic curved spacetimes that possess light disks which are made of a {\it continuum} of closed light rings. In particular, using analytical techniques which are based on the non-linearly coupled Einstein-matter field equations, we prove that these physically intriguing spacetimes contain a central compact core of radius $r_->0$ that supports an outer spherical shell with an infinite number (a continuum) of null circular geodesic which are all characterized by the functional relations $4\pi r^2_{\gamma}p(r_{\gamma})=1-3m(r_{\gamma})/r_{\gamma}$ and $8\pi r^2_{\gamma}(\rho+p)=1$ for $r_{\gamma}\in[r_-,r_+]$ [here $\{\rho,p\}$ are respectively the energy density and the isotropic pressure of the self-gravitating matter fields and $m(r)$ is the gravitational mass contained within the sphere of radius $r$].