Astrophysical Consequence of Strong Gravitational Field and its Observational Possibility

这一研究项目的目的是检查相对论效应，这可能在不久的将来在天体物理学中观察到。在赠款支持的三年中，研究了以下主题。(1)随着中子星双星在引力辐射作用下的收缩，后牛顿引力对轨道运动的影响和流体动力学效应变得更加重要。采用一个简化的模型，在模型中限制了动力学自由度，计算了并合过程中的自旋-轨道效应、自旋-自旋效应和潮汐效应。(2)计算了弱外部引力场中传播的中微子的量子力学振荡。由于波包的峰值对于显示振荡是重要的，因此对主要项进行了计算。对平直时空的结果给出了修正。然而，修正应注意能量和能量的定义等。修正的解释是微妙的，因为有重力和没有重力的时空是不同的。（3）牛顿脉动理论中的一个著名近似是忽略引力摄动的Cowling近似。在相对论性慢转恒星的精度进行了测试。结果表明，在不改变定性图象的情况下，精度较高，并在相对论中考察了轴模振荡。在旋转的最低阶，摄动方程被降低到奇异特征值问题。这意味着高阶效应对于确定空间函数很重要。实际上，描述振荡的空间函数由考林近似确定。结果表明，熵分布是决定性的。对于均匀熵分布，模被限制在某类。

The aim of this research project was to examine relativisticeffects, which may be in the near future observed in astrophysics. For three years supported by the grant, the following topics are examined.(1) As the binary of neutron stars shrinks due to gravitationalradiation, the post-Newtonian gravitational effects to the orbital motion and the hydro-dynamical effects become more important. A simplified model, in which the dynamical degrees offreedom are restricted, is adopted to evaluate the spin-orbit, spin-spin and tidal effects in the coalescence.(2) Quantum mechanical oscillation is calculated for neutrinospropagating in weak external gravitational field. Since the peak of wave packet is important to exhibit the oscillation, the main terms are evaluated. The correction to the result of flat space-time is explicitly derived. The correction should however be careful for the definition of the energy and lengt etc. The interpretation of the correction is subtle since space-times with gravity and without gravity are distinct.(3)One of well-known approximation used in the Newtonian pulsation theory is so-called the Cowling approximation in which gravitational perturbation is neglected. The accuracy in the relativistic slowly rotating stars is tested. The result shows the accuracy is fairly good without any change of the qualitative pictures.Axial mode oscillation is also examined in the relativity. At the lowest order of the rotation, the perturbation equation is reduced to singular eigen-value problem. This means that higher order effects are important to determine the spatial function. Indeed, the spatial function describing the oscillation is determined by the Cowling approximation. It is found that the entropy distribution is 'crucial. For the uniform entropy distribution, the mode is restricted to some class.