Geodesic equation in Schwarzschild-(anti-)de Sitter space-times:: Analytical solutions and applications
Geodesic equation in Schwarzschild-(anti-)de Sitter space-times:: Analytical solutions and applications
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DOI：
10.1103/physrevd.78.024035
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发表时间：
2008-07-01
影响因子：
5
通讯作者：
Laemmerzahl, Claus
中科院分区：
文献类型：
--
作者：
Hackmann, Eva;Laemmerzahl, Claus
给出了Schwarzschild-(反)de Sitter时空中测地线方程的完整解析解。这些解是从限制在被称为theta除数的theta函数的零点集合的Jacobi求逆问题中得到的。在它的最终形式中，解可以用Kleian sigma函数的导数来表示。由此产生的不同类型的轨道以守恒的能量和角动量以及宇宙常数来表征。利用解析解，解决了宇宙常数是否可能是先锋反常的原因的问题。给出了近星移位及其后Schwarzschild极限。该方法同样适用于高维Schwarzschild时空中的测地线方程。
The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti-)de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer anomaly is addressed. The periastron shift and its post-Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space-times.