论文标题
通用超级反对物体的epicyclic频率
Epicyclic Frequencies for a Generic Ultracompact Object
论文作者
论文摘要
最近，已经表明，由固定的，轴对称，渐近平坦的物体产生的时空中的径向稳定性，具有$ \ mathbb {z} _2 $对称性，确定了围绕LR的时间表状圆形圆柱（TCOS）的可能性和辐射稳定性。在本文中，我们还通过研究径向和垂直的环保频率来考虑轨道的垂直（角度）稳定性来概括这一结果。我们表明，LR的垂直稳定性仅确定周围TCO的垂直稳定性。还提供了平方环境频率和RICCI张量之间的关系。通过这种关系，我们表明具有径向和垂直不稳定的LRS（TCO）的对象违反了零（强）能量状况。
Recently, it has been shown that the radial stability of a light-ring (LR) in a spacetime generated by a stationary, axisymmetric, asymptotically flat object with a $\mathbb{Z}_2$ symmetry determines the possibility and radial stability of timelike circular orbits (TCOs) around the LR. In this paper, we generalise this result by also considering the vertical (angular) stability of the orbits through the study of the radial and vertical epicyclic frequencies. We show that the vertical stability of the LR only determines the vertical stability of the TCOs around it. A relation between the sum of the squared epicyclic frequencies and the Ricci tensor is also provided. With such relation, we show that objects with radially and vertically unstable LRs (TCOs) violate the null (strong) energy condition.
