标题： 广义相对论视角下的星系动力学观点 显示英文标题

标题： Perspectives on Galactic Dynamics via General Relativity

摘要： 我们近期发表的论文《广义相对论解决了...》所收到的问题、评论和批评的回应如下。 强调我们的模型完全自然地描述了轴对称星系的动力学，并且我们的解（尽管理想化）包含了问题的本质。 对称平面处度规导数的不连续性必然被解释为密度梯度数学理想化不连续性的结果，并且通过高斯散度定理显示出与分布体积密度的自然联系。 我们提出了论据，表明对于我们的近似弱场模型，我们可以选择物理上令人满意的质量分布，而无需伴随奇异的质量表面层。 为了支持这一观点，我们通过对移除 $z=0$ 平面附近密度梯度的不连续性的区域略微修改了解。 引入表面层的替代方案会导致出现负质量表面层，其数值接近正质量连续区域。 这与模型的假设稳定性相矛盾。 我们发现，当测试粒子接近 $z=0$ 平面时，其行为正常，加速度指向该平面的方向。 这与负质量层假设相矛盾，因为负质量会排斥测试粒子。 因此，进一步支持了我们原始模型的完整性。 显示英文摘要

摘要： Responses to questions, comments and criticism of our recent paper "General Relativity Resolves.." are provided. It is emphasized that our model is entirely natural to describe the dynamics of an axially symmetric galaxy and that our solution, albeit idealized, contains the essence of the problem. The discontinuity of the metric derivative on the symmetry plane is necessarily interpreted as the effect of the mathematically idealized discontinuity of the gradient of the density and is shown to be naturally connected to the distributed volume density via the Gauss divergence theorem. We present arguments to the effect that for our approximate weak field model, we can choose the physically satisfactory mass distribution without an accompanying singular mass surface layer. To support this contention, we modify our solution slightly by removing the discontinuity with a region of continuous density gradient overlapping the $z=0$ plane. The alternative of invoking a surface layer leads to the presence of a negative mass surface layer approaching the numerical value of the positive mass continuous region. This is in contradiction with the assumed stationarity of the model. We find that a test particle behaves normally as it approaches the $z=0$ plane, the acceleration being towards the direction of this plane. This is in contradiction to the negative mass layer hypothesis as negative mass would repel the test particle. Thus, further support is added to the integrity of our original model.