论文标题
在Schwarzschild黑洞外部的无效和类似的测量学研究的研究
Study of null and time-like geodesics in the exterior of a Schwarzschild black hole with quintessence and cloud of strings
论文作者
论文摘要
最近，参考文献中已经在参考文献中完成了对径向和圆形轨道的分析研究，该研究在参考文献中进行了参考文献中进行的。 \ cite {Mustafa：2021}。在本文中，除了考虑到未结合轨道的情况外，我们还通过调查了其他类型的绑定轨道运动方程的分析解决方案来完成上述研究。这需要对对测试粒子运动进行分类的相应有效电位的广泛研究。我们遵循标准的Lagrangian动力学来参数径向和角度测量学，并且相应处理的（超）（超）椭圆形积分。我们还模拟了与有效电位中不同水平的能量相对应的轨道。
Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has been done in Ref. \cite{Mustafa:2021}. In this paper, we complete the aforementioned study by investigating possible analytical solutions to the equations of motion for other types of bound orbits, besides taking into account the cases of unbound orbits. This requires an extensive study of the corresponding effective potentials that categorize the test particle motion. We follow the standard Lagrangian dynamics to parametrize the radial and angular geodesics and the resultant (hyper-)elliptic integrals of motion are treated accordingly. We also simulate the orbits which correspond to different levels of energy in the effective potentials.
