In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could be interpreted as a “rigid body” in general relativity and we analyze the different properties respect to the rigidly rotating disk in special relativity: for example, the general relativistic counterpart shows no Doppler effect for a light signal emitted and received from any two points at rest respect to the “rigid body”. This effect can be important to test the validity of the assumed model for our galaxy. In the second part we approach the problem from a low energy expansion perspective and we write down a generalization of the virial theorem for stationary spacetimes. The non-Newtonian contributions can lead to a re-weighting of dark matter in galaxies.

在这项工作中，我们研究了广义相对论中刚性旋转的中性尘埃溶液的性质。由于螺旋星系动力学的应用，这类解决方案最近获得了相关性。我们证明了这个类可以被解释为广义相对论中的“刚体”，我们分析了狭义相对论中刚性旋转圆盘的不同特性：例如，广义相对论对应物对发射的光信号没有多普勒效应，并且从相对于“刚体”的任何两个静止点接收。这种效应对于测试我们银河系的假设模型的有效性可能很重要。在第二部分中，我们从低能量膨胀的角度来处理这个问题，并且我们写下了平稳时空的维里定理的推广。