论文标题
来自等效2D指标的无效圆形轨道
Null and timelike circular orbits from equivalent 2D metrics
论文作者
论文摘要
在某些假设下，球形$ 1 + 3 $维数的运动可以分别由曲线在二维歧管上描述，分别用于null和时端曲线的光学和雅各比歧管。在本文中，我们求助于辅助二维指标，以研究通用静态，球体对称和渐近平坦的循环大地测量学，$ 1 + 3 $尺寸空位，其功能至少$ c^2 $平滑。这是通过研究双相等歧管的高斯曲率以及这些圆形路径上的地球曲率的方法来完成的。这项研究考虑了无效的圆形测量学。通过光歧管对无效的测量学的研究检索了黑洞外部的时空上的光环数（LRS）的已知结果，并在具有地平面紧凑物体的空位上。通过同等的步骤，我们可以对给定时空的边缘稳定的圆形轨道（TCO）制定类似的定理，满足前面提到的假设
The motion of particles on spherical $1 + 3$ dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this paper we resort to auxiliary 2-dimensional metrics to study circular geodesics of generic static, spherically symmetric, and asymptotically flat $1 + 3$ dimensional spacetimes, whose functions are at least $C^2$ smooth. This is done by studying the Gaussian curvature of the bidimensional equivalent manifold as well as the geodesic curvature of circular paths on these. This study considers both null and timelike circular geodesics. The study of null geodesics through the optical manifold retrieves the known result of the number of light rings (LRs) on the spacetime outside a black hole and on spacetimes with horizonless compact objects. With an equivalent procedure we can formulate a similar theorem on the number of marginally stable timelike circular orbits (TCOs) of a given spacetime satisfying the previously mentioned assumption
