Astrophysical Consequence of Strong Gravitational Field and its Observational Possibility

这个研究项目的目的是检验相对论效应，这可能在不久的将来在天体物理学中被观测到。在三年的资助期内，研究人员将研究以下课题：(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和流体动力学的影响变得更加重要。采用限制动力学自由度的简化模型，对聚并过程中的自旋-轨道效应、自旋-自旋效应和潮汐效应进行了计算。(2)计算了弱外引力场中中微子传播的量子力学振荡。由于波包的峰值对显示振荡很重要，因此对主要项进行了评估。明确地推导了对平坦时空结果的修正。然而，修正时应注意能量和长度等的定义。对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)牛顿脉动理论中使用的一个著名的近似是所谓的考林近似，其中忽略了引力摄动。对相对论性慢旋转恒星的准确性进行了测试。结果表明，在不改变定性图像的情况下，该方法具有较好的精度。在相对性中还研究了轴向模态振荡。在旋转的最低阶，微扰方程被简化为奇异特征值问题。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是由考林近似决定的。发现熵的分布是至关重要的。对于均匀熵分布，模态被限制在某一类。

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.