慢转极紧Tolman VII时空中零测地线的捕获
Trapping of null geodesics in slowly rotating extremely compact Tolman VII spacetimes
摘要：
由于引力波或中微子的捕获，隐藏在极其紧凑的物体内部的被捕获的零测地线区域具有天体物理学的重要性。对于球对称的极紧天体，零测地线的俘获效应得到了广泛的研究。最近，在具有均匀能量密度分布和均匀发射率分布的零测地线的内部线性化\mbox{Hartle--Thorne}时空的最简单可能模型中，处理了极紧凑物体的旋转对零测地线捕获的影响。在这里，我们扩展的情况下，线性化的\mbox{Hartle--Thorne}时空的捕获效果的旋转影响的研究托尔曼VII球对称的解决方案的基础上，我们假设零测地线的发射率成正比的能量密度的托尔曼VII对象具有二次径向轮廓。我们证明增强（抑制）的捕获效果的情况下，反向旋转（同向旋转）零测地线由于行为的有效电位和逃逸锥的零测地线的线性化哈特尔-索恩-托尔曼七时空。在依赖于这些时空的参数，我们确定的“本地”和“全球”系数的效率的捕获和比较的结果与旋转时空的基础上的内部史瓦西时空。我们证明，在托尔曼VII时空的捕获是更有效的，被允许在对象的半径大于那些捕获内部史瓦西时空，甚至发生在$R>3.3M$。
英文摘要：
Region of trapped null geodesics hidden inside of extremely compact objects is of astrophysical importance because of trapping of gravitational waves, or neutrinos. The trapping effect of null geodesics was extensively studied for spherically symmetric extremely compact objects. Recently, influence of rotation of the extremely compact objects on the trapping of null geodesics was treated in the simplest possible model of internal linearised \mbox{Hartle--Thorne} spacetime with uniform energy density distribution and uniform emissivity distribution of null geodesics. Here we extend the study of the rotation influence on the trapping effect in the case of linearized \mbox{Hartle--Thorne} spacetimes based on the Tolman VII spherically symmetric solutions, where we assume the emissivity of the null geodesics proportional to the energy density of the Tolman VII object having quadratic radial profile. We demonstrate enhancement (suppression) of the trapping effect in the case of counter-rotating (co-rotating) null geodesics due to the behavior of the effective potentials and escape cones of the null geodesics in the linearised Hartle--Thorne--Tolman VII spacetimes. In dependence on the parameters of these spacetimes we determine the "local" and "global" coefficients of efficiency of the trapping and compare the results to those related to the rotating spacetimes based on the internal Schwarzschild spacetimes. We demonstrate that in the Tolman VII spacetimes the trapping is more efficient, being allowed in objects with radii larger than those of the trapping internal Schwarzschild spacetimes, occurring even for $R>3.3M$.
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