Study On The Motion Of Test Particle In Reissner-Nordstr(?)m Space-Time

In this paper,the motion law of test particles in ReissnerNordstr?m space-time is studied,and the precession problem of test particles in Reissner-Nordstr?m space-time is studied by using the Action-Angle Variables.Firstly,we start with Lagrange equation and introduce some knowledge of theoretical mechanics related to this paper,including canonical equation,canonical transformation,Hamilton-Jacobian equation and Action-Angle Variables.These contents provides a theoretical basis for the follow-up study of the trajectory and perihelion precession of test particles.Then,based on Einstein’s field equation,the Reissner-Nordstr?m metric and these complete dynamic differential equations of the test particles are introduced and derived in detail.Then the energy,Lagrangian quantity and effective potential energy of the test particles are given according to the dynamic equations.According to the energy of the experimental particle,the trajectory of the particle is discussed.The analytical solution of the particle trajectory in the form of Jacobi elliptique function and the trajectory of these partial test particles around the black hole in a specific black hole space-time are given.Finally,according to the complete dynamic differential equations of the test particle,the perihelion precession of the test particle in Reissner-Nordstr?m space-time is studied by using the Action-Angle Variables.The analytical solutions of the perihelion precession of the test particle after a period in elliptical orbit and near circular orbit are given respectively.The precession analytical solution in the near circular orbit is consistent with the conclusion of the related literature in the lower order approximation.When the charge of the black hole is zero,the solution can return to the precession solution of the test particle in the near circular orbit in Schwarzschild space-time.