标题： 时空曲率的梯度流可视化 III：克尔度规与自旋参数的过渡值 显示英文标题

标题： Visualizing Spacetime Curvature via Gradient Flows III: The Kerr Metric and the Transitional Values of the Spin Parameter

摘要： 克尔度规是爱因斯坦场方程最重要的解之一，描述了旋转黑洞外部的引力场。 我们通过对协变梯度场的分析和可视化，彻底研究了克尔时空的曲率标量不变量。 我们发现，视界外的克尔几何结构在外旋转参数的值改变时会发生定性的变化，这一事实以前未知。 沿着旋转轴，曲率不变量梯度场的可观察临界点数量在几个过渡参数值处发生变化。 这些过渡值是克尔度规的一个基本属性。 它们在物理上很重要，因为在广义相对论中，这些曲率不变量以观察者无关的方式表示了旋转黑洞的整体潮汐效应和拖拽效应。 显示英文摘要

摘要： The Kerr metric is one of the most important solutions to Einstein's field equations, describing the gravitational field outside a rotating black hole. We thoroughly analyze the curvature scalar invariants to study the Kerr spacetime by examining and visualizing their covariant gradient fields. We discover that the part of the Kerr geometry outside the black hole horizon changes qualitatively depending on the spin parameter, a fact previously unknown. The number of observable critical points of the curvature invariants' gradient fields along the axis of rotation changes at several transitional values of the spin parameter. These transitional values are a fundamental property of the Kerr metric. They are physically important since in general relativity these curvature invariants represent the cumulative tidal and frame-dragging effects of rotating black holes in an observer-independent way.