论文标题
Kerr-Newman Black Hole外观的无效和时间般的大地测量学
Null and time-like geodesics in Kerr-Newman black hole exterior
论文作者
论文摘要
我们在Kerr-Newman黑洞的外部分别研究光和中性颗粒的无效测量学和中性颗粒。已知地球方程被称为一组一组一阶微分方程，可以在其中定义角度和径向电势。我们将这两种电势的根分类，并主要集中在径向电位上，重点是从黑洞的电荷产生的影响。然后，我们从椭圆形积分和null和类似时间样的大地学的椭圆形积分和雅各布椭圆函数方面获得轨迹的解，这显然是Mino时间的真实功能，即可以明确指定初始条件。我们还描述了如何将这些解决方案减少到球形轨道的情况下的细节。黑洞电荷的效果减少了直接和逆行运动的光和粒子球形运动的半径。特别是，由于框架从后孔的旋转拖动并从黑洞的电荷效果中，我们专注于球形轨道的光/粒子回旋镖。为了维持光线的方位角的变化，例如在整个行程中$ δϕ =π$，黑洞的存在降低了轨道的半径，因此减少了黑洞自旋的所需值。至于粒子飞旋镖，与光向飞旋镖相比，粒子的惯性使角度$ δϕ $的变化较小。此外，黑洞的电荷还会导致粒子的角度较小的角度变化$ δϕ $，而Kerr案中的角度也会更小。讨论了获得的结果对观察的含义。
We study the null and time-like geodesics of the light and the neutral particles respectively in the exterior of Kerr-Newman black holes. The geodesic equations are known to be written as a set of first-order differential equations in Mino time from which the angular and radial potentials can be defined. We classify the roots for both potentials, and mainly focus on those of the radial potential with an emphasis on the effect from the charge of the black holes. We then obtain the solutions of the trajectories in terms of the elliptical integrals and the Jacobian elliptic functions for both null and time-like geodesics, which are manifestly real functions of the Mino time that the initial conditions can be explicitly specified. We also describe the details of how to reduce those solutions into the cases of the spherical orbits. The effect of the black hole's charge decreases the radii of the spherical motion of the light and the particle for both direct and retrograde motions. In particular, we focus on the light/particle boomerang of the spherical orbits due to the frame dragging from the back hole's spin with the effect from the charge of the black hole. To sustain the change of the azimuthal angle of the light rays, say for example $Δϕ=π$ during the whole trip, the presence of the black hole's charge decreases the radius of the orbit and consequently reduces the needed values of the black hole's spin. As for the particle boomerang, the particle's inertia renders smaller change of the angle $Δϕ$ as compared with the light boomerang. Moreover, the black hole's charge also results in the smaller angle change $Δϕ$ of the particle than that in the Kerr case. The implications of the obtained results to observations are discussed.
