Study On The Precession Of Kerr-Newman Spacetime And Application Of The Lie Series Method To The Two-body Problem

In Einstein’s theory the spacetime is thought as a four dimensional pseudo-Riemannian manifold whose geometry interacts nonlinearly with matter.Because of this feature,in general calculations in General Relativity(GR)require much more work than the corresponding ones in Newtonian gravity and this fact has made more difficulty the understanding of the physics of Einsteinian gravity.Another consequence of this difficulty falls in the context of testing Einstein’s gravity: our inability to solve general the gravitational field equations limits the possibility of devising full tests of GR.We can only calculate from the solutions of Einstein’s field equations with symmetry or from the postNewtonian approximation.The work of this thesis is divided into two main parts as follows.In the first part,the problem of precession of the test particle on the equatorial plane in the Kerr-Newman metric in Boyer-Lindquist coordinates is studied.Starting from the Hamiltonian of the Kerr-Newman metric.The Hamiltonian are substituted into the Hamilton-Jacobi equation,and the coordinates of the angle of action variables are defined after separating the variables of the fully integrated equation,and the incoming expression of a test particle is finally solved by the theory of the Angleaction variables.In the second part,we analyze the problem of relativistic two-body problem with spin employing a perturbation scheme based on Lie series.Starting from a post-Newtonian expansion of the Einstein field equationsand our method takes into full account the complex interplay between the various relativistic effects.Simplify the Hamiltonian and substitute it into the Hamilton canonical equation a new explicit solution of motion expressed by elliptic function is obtained.