Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
复制标题
克尔时空中束缚类时测地轨道的解析解
DOI：
10.1088/0264-9381/26/13/135002
复制
发表时间：
2009
影响因子：
3.5
通讯作者：
W. Hikida
中科院分区：
文献类型：
--
作者：
R. Fujita;W. Hikida
我们推导了克尔时空中束缚类时测地轨道的解析解。解析解以米诺时间 λ 作为自变量的椭圆积分表示。米诺时间解耦了粒子的径向运动和极向运动，因此产生了更有用的形式来估计克尔时空中束缚类时测地线的三个基本频率（径向、极向和方位角运动）。本文给出了基频解析表达式的一阶推导。本文还给出了使用米诺时间的束缚类时测地线所有坐标的解析表达式的一阶推导。这些解析表达式不仅对于研究克尔测地线的物理性质有用，而且更重要的是对于与根据极端质量比螺旋估计引力波相关的应用有用。
We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time λ as the independent variable. Mino time decouples the radial and the polar motion of a particle and hence leads to forms more useful to estimate three fundamental frequencies, radial, polar and azimuthal motion, for the bound timelike geodesics in Kerr spacetime. This paper gives the first derivation of the analytical expressions of the fundamental frequencies. This paper also gives the first derivation of the analytical expressions of all coordinates for the bound timelike geodesics using Mino time. These analytical expressions should be useful not only to investigate physical properties of Kerr geodesics but more importantly to applications related to the estimation of gravitational waves from the extreme mass ratio inspirals.