The Motion Of A Test Particle In The Theory Of General Relativity

It is well known that, Newton's gravitational theory has some intrinsic difficulties, such as the non-Lorentz covariant of the gravitational field, the orbital precession of Mercury etc.. The establishment of the theory of general relativity solved these difficulties. The new features introduced by the theory of general relativity are called generally relativistic gravitation effects. In this paper, we studied the precession and gravitation acceleration effects of a test particle in gravitational fields.Starting the equations of motion of a test particle in gravitational fields, and supposing the orbit of a test particle is the conics, we derived the formulae of orbital precession in the Schwarzschild spacetime and in the spacetime with the magnetic dipole and the electric charge, and discussed the physical meanings. For the orbital precession of a test particle in the spacetime with the magnetic dipole and the electric charge, we are interested in the effects of the magnetic dipole on the orbital precession. We found that when the magnetic dipole L is small, it hardly affects the orbitalprecession;but when the magnetic dipole L increases, it affects the orbital precession. Especially, the precession reversed its direction, when the magnetic dipole L is of order 1017 m2 (in units of G-c = l).From the geodesies, and by introducing local Lorentz spacial section, we investigated the acceleration effects of a test particle in the time-dependent de-sitter spacetime, and discussed the relation between the acceleration of a test particle and dm/dv. We found that when dm/dv<0,the Ag<0 (i. e.the gravitation acceleration decreases), and when dm/dv>0, the Ag>0.