Astrophysical Consequence of Strong Gravitational Field and its Observational Possibility

这项研究项目的目的是检验在不久的将来可能在天体物理学中观察到的相对论效应。在该基金资助的三年中，我们研究了以下问题：(1)由于引力辐射导致中子星的双星收缩，后牛顿引力效应对轨道运动的影响和流体动力学效应变得更加重要。采用动力学自由度受限的简化模型，计算了中微子在弱引力场中的自旋轨道、自旋自旋和潮汐效应。(2)计算了中微子在弱引力场中传播的量子力学振荡。由于波包的峰值是表现振荡的重要因素，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，修正应该注意能量和长度等的定义。修正的解释是微妙的，因为有引力和无引力的时空是不同的。(3)牛顿脉动理论中使用的著名近似之一是所谓的考林近似，其中忽略了引力扰动。对相对论慢速自转恒星的精度进行了测试。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，并从相对论的角度考察了轴模振荡。在旋转的最低阶处，摄动方程化为奇异本征值问题。这意味着高阶效应是决定空间函数的重要因素。实际上，描述这种振荡的空间函数是由考林近似确定的。结果表明，熵分布是至关重要的，对于均匀的熵分布，模被限制在某一类。

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.