Analytic solutions of equations of motion in General Relativity

广义相对论运动方程的解析解

• 批准号: 157461990
• 负责人: Professorin Dr. Jutta Kunz-Drolshagen
• 金额: --
• 依托单位: Zentrum für angewandte Raumfahrttechnologie und Mikrogravitation (ZARM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/157461990?language=en
• 关键词: Analytic; solutions; equations; motion; General

There are only very few analytic solutions known for the geodesic equation in black hole space–times. They are given by elliptic functions. Based on our recent work (1, 2, 3) where we worked out a new method yielding analytic solutions in terms of hyperelliptic functions based on polynomials of 6th order and restricted to the theta–divisor, we intend to find the complete set of analytic solutions in all Plebański–Demiański black hole space–times which includes Kerr–de Sitter, for example, and also to higher dimensional axially symmetric space–times. We also intend to apply this method to the geodesic motion of point particles in axially symmetric mass multipole field and also to particles with spin and mass quadrupole moment and to strings. This new method should be extended to higher order polynomials. Based on these analytical solutions all possible physical effects like Perihelion shift, deflection angles, Lense–Thirring effect, etc. can be given analytically. Analytic solutions of the geodesic equation are important for a physical interpretation of space–times, can be used for solving the effective one–body dynamics of binary systems yielding gravitational wave templates, may serve as test bed for numerical codes, and has practical applications in geodesy and navigation.

已知的黑洞时空中测地线方程的解析解很少。它们是由椭圆函数给出的。在我们最近的工作(1，2，3)的基础上，我们提出了一种新的方法，以6次多项式为基础，并限制在theta因子上，得到了超椭圆函数形式的解析解。我们打算在所有的Plebański-Demiański黑洞时空(例如，包括Kerr-de Sitter)以及高维轴对称时空中找到完整的解析解集。我们还打算将该方法应用于点粒子在轴对称质量多极场中的测地线运动，以及具有自旋和质量四极矩的粒子以及弦。这种新方法应该推广到高次多项式。基于这些解析解，可以解析地给出近日点移动、偏转角、透镜-瑟林效应等所有可能的物理效应。测地线方程的解析解对于时空的物理解释很重要，可以用来求解产生引力波模板的双星系统的有效单体动力学，可以作为数值代码的试验台，在大地测量和导航中有实际应用。

项目成果

Dynamics of test particles in thin-shell wormhole spacetimes

薄壳虫洞时空中测试粒子的动力学

• DOI: 10.1088/0264-9381/30/17/175014
• 发表时间: 2013
• 期刊: Classical and Quantum Gravity
• 影响因子: 3.5
• 作者: V. Diemer (née Kagramanova);E. Smolarek
• 通讯作者: E. Smolarek

Charged particle motion in Kerr-Newmann space-times

• DOI: 10.1103/physrevd.87.124030
• 发表时间: 2013-04
• 期刊: Physical Review D
• 影响因子: 5
• 作者: E. Hackmann;H. Xu

Observables for bound orbital motion in axially symmetric space-times

• DOI: 10.1103/physrevd.85.044049
• 发表时间: 2011-07
• 期刊: Physical Review D
• 影响因子: 5
• 作者: E. Hackmann;C. Lammerzahl

Analytic treatment of geodesics in five-dimensional Myers-Perry space-times

• DOI: 10.1103/physrevd.86.084029
• 发表时间: 2012-08
• 期刊: Physical Review D
• 影响因子: 5
• 作者: V. Kagramanova;Stephan Reimers