标题： 宇宙学涡度扰动、引力磁效应和马赫原理 显示英文标题

标题： Cosmological Vorticity Perturbations, Gravitomagnetism, and Mach's Principle

摘要： 陀螺仪的轴线实验上定义了非旋转参考系。 但什么物理原因决定了陀螺仪轴线的时间演化？ 从一个未受扰动、空间平坦的FRW宇宙学出发，我们考虑在一级近似下的宇宙涡旋扰动（即矢量扰动、旋转扰动）。 我们的问题是：宇宙的旋转扰动是否会相对于超出旋转扰动方向（测地线）的星系方向拖拽陀螺仪的轴线？ 我们将引力磁学的定律转化为一种形式，清楚地显示出与普通磁学定律之间的密切对应关系。 我们的结果是：1）由超出$\dot{H}$半径（H = 哈勃常数）的旋转扰动对陀螺仪轴线的拖拽是指数抑制的。 2）如果扰动是在显著大于$\dot{H}$半径内的均匀旋转，则对于宇宙物质的任何状态方程，旋转扰动对陀螺仪轴线的拖拽是精确的。 3）对于任何状态方程，陀螺仪轴线的时间演化精确地遵循$\dot{H}$半径内物质的一个特定平均值。 在这种精确的意义上，马赫原理可以从爱因斯坦引力的宇宙学中得出。 显示英文摘要

摘要： The axes of gyroscopes experimentally define non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed, spatially flat FRW cosmology, we consider cosmological vorticity perturbations (i.e. vector perturbations, rotational perturbations) at the linear level. We ask: Will cosmological rotational perturbations drag the axis of a gyroscope relative to the directions (geodesics) to galaxies beyond the rotational perturbation? We cast the laws of Gravitomagnetism into a form showing clearly the close correspondence with the laws of ordinary magnetism. Our results are: 1) The dragging of a gyroscope axis by rotational perturbations beyond the $\dot{H}$ radius (H = Hubble constant) is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a radius significantly larger than the $\dot{H}$ radius, then the dragging of the gyroscope axis by the rotational perturbation is exact for any equation of state for cosmological matter. 3) The time-evolution of a gyroscope axis exactly follows a specific average of the matter inside the $\dot{H}$ radius for any equation of state. In this precise sense Mach's Principle follows from cosmology with Einstein Gravity.