论文标题
牛顿电势中的粒子动力学由均匀的圆环产生
Particle dynamics in the Newtonian potential sourced by a homogeneous circular ring
论文作者
论文摘要
如果空间尺寸均匀，则由任意维欧几里得空间中的均匀圆形环采用的牛顿引力电势会采用简单的形式。相反，如果空间维度很奇怪，则以包含完整椭圆积分的形式给出。在本文中，我们分析了牛顿潜力中自由掉落的粒子的动力学。着眼于放置环的对称平面上的圆形轨道，我们观察到它们在4D空间及以上是不稳定的，而它们在3D空间中稳定。稳定的圆形轨道的序列以$ 1.6095 \ cdots的$乘以$乘以环的半径，这对应于最内向的稳定圆形轨道（ISCO）。在环的对称性轴上，3D空间中没有圆形轨道，但比4D空间中没有圆形轨道。特别是，在4D空间中的ISCO和INFINITY之间以及ISCO和5D空间中最外面稳定的圆形轨道之间的圆形轨道是稳定的。 6D空间及以上没有稳定的圆形轨道。
Newtonian gravitational potential sourced by a homogeneous circular ring in arbitrary dimensional Euclidean space takes a simple form if the spatial dimension is even. In contrast, if the spatial dimension is odd, it is given in a form that includes complete elliptic integrals. In this paper, we analyze the dynamics of a freely falling massive particle in its Newtonian potential. Focusing on circular orbits on the symmetric plane where the ring is placed, we observe that they are unstable in 4D space and above, while they are stable in 3D space. The sequence of stable circular orbits disappears at $1.6095\cdots$ times the radius of the ring, which corresponds to the innermost stable circular orbit (ISCO). On the axis of symmetry of the ring, there are no circular orbits in 3D space but more than in 4D space. In particular, the circular orbits are stable between the ISCO and infinity in 4D space and between the ISCO and the outermost stable circular orbit in 5D space. There exist no stable circular orbits in 6D space and above.
