Albert Einstein is one of the most famous physicists in the world, who formulated an equation to explain the most fundamental interactions of gravitation called the Einstein field equation. Due to the complexity in solving the Einstein field equation, it is accepted that some assumption must be made to reduce the complexity. One of the most popular assumptions is that of a perfect fluid sphere. It is simply performed to simulate the realistic stars. In this thesis, we introduce another method which is based on perfect fluid spheres to solve for the exact solutions. Using pure mathematical principles to construct this method, it is thus called as the solution generating theorems. In currently, we will study these solutions in the isotropic coordinates. We derive a new theorem and a corollary that map a perfect fluid sphere into another perfect fluid sphere, and then we analyze those properties of the perfect fluid spheres. Moreover, we apply this theorem with some example solutions in program Maple. Especially, we also present a new technique for the generation of perfect fluid spheres. Eventually, we obtain a new modified TOV equation, which is an equation to explain the internal structure of realistic stars such as the pressure, density, and mass profiles.

Thesis (M.Sc.)--Chulalongkorn University, 2015