The curvature invariants have been the subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a fundamental difference between the gravitomagnetic fields arising from the translational and rotational motions of the sources (which have been subject of observational and experimental tests, including the dedicated Gravity Probe-B and LARES space missions). In this work we clarify both the algebraic and physical meaning of the curvature invariants and their electromagnetic counterparts. They are seen to yield conditions for the existence of observers measuring vanishing electric/magnetic fields and gravitoelectric/gravitomagnetic tidal tensors, respectively. We determine these observers (in the gravitational sector and in the presence of sources, for the more relevant gravitomagnetic case) obtaining their velocities explicitly in terms of the fields/tidal tensors as measured by an arbitrary observer. The structure of the invariants of the astrophysical setups of interest is studied in detail, and its relationship with the gravitomagnetic effects is dissected. Finally, a new classification for intrinsic/extrinsic gravitomagnetism is proposed.

中文翻译：

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引力磁性和曲率标量不变量的意义

由于关于内在/外在坐标系拖拽的概念、在这种分类中使用电磁类比的争论，以及由引力场产生的引力磁场之间是否存在根本区别的问题，曲率不变量一直是人们感兴趣的主题。源的平移和旋转运动（已成为观测和实验测试的主题，包括专用的重力探测器-B 和 LARES 太空任务）。在这项工作中，我们阐明了曲率不变量及其电磁对应项的代数和物理意义。它们被认为为观测者分别测量消失的电场/磁场和重力/重力潮汐张量提供了条件。我们确定这些观察者（在引力区和存在源的情况下，对于更相关的引力磁情况），根据任意观察者测量的场/潮汐张量明确获得它们的速度。详细研究了感兴趣的天体物理设置的不变量的结构，并剖析了其与重磁效应的关系。最后，提出了一种新的内/外重磁分类。