分布性能量四极的张量表示及其动力学
The tensorial representation of the distributional stress-energy quadrupole and its dynamics
AI总结：
本文研究了由世界线上δ函数协变导数构造的应力-能量张量，推导了至四极阶的动力学方程，并证明了多极子分量的唯一性及其与张量场标准矩的关系。
摘要：
我们研究了由世界线上狄拉克δ函数的协变导数构造的应力-能量张量。由于使用了协变导数，所有分量均按张量方式变换。我们推导了直至四极阶的分量动力学方程。然而，这些分量确实以非张量的方式依赖于沿世界线选择的矢量。我们还推导了关于一般多极子的若干重要结果，包括其分量是唯一的，且所有多极子均可用协变导数写出。我们通过平行移动该张量场，展示了多极子分量与张量场标准矩之间的关系。
英文摘要：
We investigate stress-energy tensors constructed from the covariant derivatives of delta functions on a worldline. Since covariant derivatives are used all the components transform as tensors. We derive the dynamical equations for the components, up to quadrupole order. The components do, however, depend in a non-tensorial way, on a choice of a vector along the worldline. We also derive a number of important results about general multipoles, including that their components are unique, and all multipoles can be written using covariant derivatives. We show how the components of a multipole are related to standard moments of a tensor field, by parallelly transporting that tensor field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
