弯曲时空中检验粒子的运动  

Motion of Test Particles in Curved Spacetime

作　　者：袁业飞[1] YUAN Ye-Fei(CAS Key Laboratory for Research in Galaxies and Cosmology,Department of Astronomy,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学天文学系中国科学院星系与宇宙学重点实验室,安徽合肥230026

出　　处：《安徽师范大学学报（自然科学版）》2018年第5期409-414,共6页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金杰青项目(11725312)

摘　　要：在经典广义相对论中,引力其实是一种几何效应,即所谓的引力几何化。在本文中,我们通过研究弯曲时空中检验粒子的运动,来阐述引力几何化的基本思想。我们的基本观点是:在弯曲时空中,检验粒子除了受到弯曲时空的影响,不受任何其它力的作用,类似于平直空间中的自由粒子,检验粒子的拉格朗日量仅含动能项–四维弯曲空间的动能项。以球对称弯曲时空为例,在时空弯曲很小的情况下,即弱场近似下,该拉格朗日量退化为牛顿力学中球对称引力场中的拉格朗日量,其中的引力势与描写时空弯曲效应的时空度规有关,即引力是几何化的。In the classical general theory of relativity,gravity is actually a geometric effect,i.e.the so-called geometrization of gravitation.In this paper,we elaborate the basic idea of geometrization of gravitation by investigating the motion of test particles in curved spacetime.Our basic point of view is that in the curved space-time,the Lagrangian of test particles contains only their kinetic energy in the four dimensional curved spacetime,which is similar to the case in the flat spacetime.In spherically curved spacetime,if the curvature of spacetime is very small,that is,in the regime of weak field,the original Lagrangian reduces into the Newtonian Lagrangian of test particles in the spherically symmetric gravitational field,and the gravitational potential is relevant to the metric of the spacetime which describes the curvature of spacetime.In a word,the gravitation is geometrized.

关 键 词：拉格朗日量 广义相对论 弯曲时空 

分 类 号：O412.1[理学—理论物理]