通过框架阻力涡和潮汐趋势可视化时空曲率I。一般理论与弱引力应用
Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications
摘要：
当我们将时空分裂为空间加时间时，外尔曲率张量（真空黎曼张量）分裂为两个空间的、对称的、无迹（STF）张量：（i）外尔张量的所谓“电”部分或潮汐场，（ii）外尔张量的所谓“磁”部分或框架-拖曳场。作为STF，潮汐场和框架阻力场各有三个正交的特征向量场，可以用它们的积分曲线来描述。我们把潮汐场特征向量的积分曲线称为趋势线，把每条趋势线的特征值称为趋势，把具有大趋势的趋势线的集合称为趋势线。与框架阻力场类似的量是涡线、涡度和涡。通过将这些概念应用于各种弱引力现象，我们建立了对这些概念的物理直觉：一个旋转的引力点粒子，两个这样的粒子并排，一个平面引力波，一个具有动力学电流四极矩或动力学质量四极矩的点粒子，以及一个由非旋转点粒子组成的慢运动双星系统。[摘要是缩写的;完整的摘要还提到了其他结果。]
英文摘要：
When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free (STF) tensors: (i) the Weyl tensor's so-called "electric" part or tidal field, and (ii) the Weyl tensor's so-called "magnetic" part or frame-drag field. Being STF, the tidal field and frame-drag field each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of the tidal field's eigenvectors tendex lines, we call each tendex line's eigenvalue its tendicity, and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for the frame-drag field are vortex lines, their vorticities, and vortexes. We build up physical intuition into these concepts by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side by side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. [Abstract is abbreviated; full abstract also mentions additional results.]
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。
