论文标题
黑洞测量学的动作角度坐标I：球形对称和Schwarzschild
Action-angle coordinates for black-hole geodesics I: Spherically symmetric and Schwarzschild
论文作者
论文摘要
动作角坐标是一种在天体力学中常用的工具，可系统地参数化和存储天体物理体运动方程的一般解。 I使用后圆形膨胀在静态的，球体对称的空间时间中构造构造的动作角度坐标，以进行固定的测试粒子运动。然后，我将施瓦茨柴尔德黑孔引力场中运动的表达式专长，并为哈密顿尔顿人提供明确的公式，以归功于径向动作中的第10个功率（偏心率第20次功率），而角度坐标则与相对性或相对性的或相对性的或相对性的或相对性的或相对性的或相对性的或谐波。该结果为通过坐标时间参数的轨道运动提供了封闭形式的扰动解决方案，该解决方案将在紧凑型二元灵感和其他天体物理学领域的建模中找到应用。
Action-angle coordinates are a tool commonly used in celestial mechanics to systematically parametrize and store general solutions of the equations of motion of astrophysical bodies. I perturbatively construct action-angle coordinates for bound test particle motion in static, spherically symmetric space-times using a post-circular expansion. Then I specialise the expressions to the motion in the gravitational fields of Schwarzschild black holes and give explicit formulas for the Hamiltonian to the 10th power in the radial action (20th power in eccentricity), and the transformation to angle coordinates up to the 8th harmonic with respect to a relativistic orbital anomaly. The results provide a closed-form perturbative solution for the orbital motion parametrized by coordinate time that will find applications in the modelling of compact binary inspirals and other fields of astrophysics.
