Solution Generating Theorems and Tolman-Oppenheimer-Volkov Equation for Perfect Fluid Spheres in Isotropic Coordinates

摘要

Despite the possibility of finding exact solutions to the Einstein field equations, there is another way to obtain new exact solutions without having to directly solve the Einstein field equations. This method is the so called "solution generating theorems". In the descriptive approximation of stars, we will bring these solutions to analyze the realistic stars. One of the popular assumptions is a perfect fluid sphere. The Tolman-Oppenheimer-Volkov (TOV) equation describes the internal structure of general relativistic static perfect fluid spheres, including the pressure and density profiles. In this paper, we find relative solution generating theorems that map perfect fluid spheres into perfect fluid spheres in isotropic coordinates. In addition, we study and develop new solutions for the TOV equation.