الفهرس | Only 14 pages are availabe for public view |
Abstract This thesis is concerning with the computation of the energy and linear momentum density at any point of curved spaces relative to a local coordinate system . Indeed the curved space under consideration is so-called rotational symmetric space-time. The property of the rotational symmetry is hidden but it is existed via some killing vector in the direction of one of the three axes. In the first chapter, we introduce the basic definitions and some theorems from differential geometry, tensors, electromagnetic field theory and the geometry of the special relativity. Maxwell equations have coupled property in calculating the components of the electromagnetic field. Therefore we introduced the definition of null tetrad, its properties and its relations with the differential operators generally. This helps us to calculate the coordinates of the electromagnetic field in any curved space. Chapter 2 We achieved the general decoupled wave form of the potential equation. The coefficients of the terms in the wave equation are very long because of two reasons . First, the functions in the coefficients of the line element are not given explicitly. Second, the equations are considered as a general method for calculating the electromagnetic fields components. Chapter 3 We obtained a separable solution of the potential equation and we used the general potential in obtaining the components of the electromagnetic field , the energy and the linear momentum densities at any point of the space via the so-called Pointing vector. Finally, we considered the special case when the rotational symmetric distance is conformally flat. |