We consider a binary system of spinning compact objects with internal structure, moving along an exactly circular orbit, and modeled within the multipolar gravitational skeleton formalism, up to quadrupolar order. We prove that the worldline of each multipolar particle is an integral curve of the helical Killing vector field, and that the four-velocity, four-momentum, spin tensor and quadrupole tensor of each particle are Lie-dragged along those worldlines. The geometrical framework developed in this paper paves the way to an extension of the first law of compact-object binary mechanics up to quadrupolar order.

中文翻译：

---

螺旋对称时空中的多极粒子

我们考虑具有内部结构的旋转紧凑物体的二元系统，沿着精确的圆形轨道移动，并在多极引力骨架形式主义中建模，达到四极阶。我们证明了每个多极粒子的世界线是螺旋Killing矢量场的积分曲线，并且每个粒子的四速度、四动量、自旋张量和四极张量都沿这些世界线Lie-drag。本文开发的几何框架为将紧凑物体二元力学第一定律扩展到四极阶铺平了道路。