الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The gravitational fields of some elementary mass system were discussed in several references and papers. For example the Schwarzchild solution, the Kerr solution and Tomimatsu-Sato metric [1]. In this thesis the solution of the Einstein equations for axial symmetric is presented. For example the vVeyl-Levi-Civita metric describing a field with rotational symmetry is presented and discussed from some points of view.
This thesis which is consisting of three chapters is concerning with” The effect of 8u’(ial symmetric metric on the scalar field behavior”. Indeed, the property of the axial symmetric is a reflection of a hidden symmetry which is due to the rotational symmetry and not known spherical symmetry.
In the first chapter we introduced some known definitions from differential geommetry and relativity which are used throughout the thesis.
In the second chapter we consider the line element in the rotational symmetric curved space-time in it’s general form and it’s reduced form.We substituted Crystofell symbols of the second kind in the Klien-Gordon covariant form equation. Because the functions in the metric tensor are not given explicitly we obtained particular solution using the idea of separation of variables. Furthermore we succeeded in finding a class of solutions of the empty Einstein field equations under some conditions. Finally in this chapter we obtained the behavior of free particle in the rotational symmetric curved space time.
In chapter three we considered the accelerated frame of reference. In this space time we obtained the equation of motion of free particle via the Crystofell symbols which are obtained by comparing the geodesic equations with the Euler-Lagrange equations of motion. Finally, we comparecl the motion of free particle in the last two chapters.