论文标题
Kerr Spacetime中的轴上潮汐力
On-Axis Tidal Forces in Kerr Spacetime
论文作者
论文摘要
潮汐力是与曲率张量有关的一般相对性的重要特征。我们分析了Kerr时空中的潮汐张量，重点是沿Kerr Black Hole的对称轴的情况，并指出，与Schwarzschild SpaceTime不同，使用Boyer-Lindquist坐标，潮汐力可能会在某个点上消失。我们详细研究了沿对称轴尘埃中插入的体内消失的潮汐力的影响。我们找到了地球偏差方程并在数值和分析上解决它们，以沿着Kerr几何形状的对称轴运动。我们还指出，对称轴处事件范围内的内在高斯曲率等于沿那里的潮汐张量的该轴的分量。
Tidal forces are an important feature of General Relativity, which are related to the curvature tensor. We analyze the tidal tensor in Kerr spacetime, with emphasis on the case along the symmetry axis of the Kerr black hole, noting that tidal forces may vanish at a certain point, unlike in the Schwarzschild spacetime, using Boyer-Lindquist coordinates. We study in detail the effects of vanishing tidal forces in a body constituted of dust infalling along the symmetry axis. We find the geodesic deviation equations and solve them, numerically and analytically, for motion along the symmetry axis of the Kerr geometry. We also point out that the intrinsic Gaussian curvature of the event horizon at the symmetry axis is equal to the component along this axis of the tidal tensor there.
