Authors: Tritos Ngampitipan, Petarpa Boonserm and Apisit Kinreewong
Abstract: The Einstein field equation describes the relationship between spacetime geometry and matter (or energy). In general, the equation cannot be solved because of its extreme complexity. Therefore, several related methods have been developed to find the solution. In the article [Phys. J. Vol. 2, No. 2, 2016], the Riccati equation has been used to develop a method to obtain new solutions for perfect fluid spheres in the curvature coordinates. In this pape r, we focus on the use of the Riccati equation in finding new solutions for perfect fluid spheres in isotropic coordinates. Moreover, we also present another method, the Fourier transform, to obtain new solutions. The Schwarzschild metric is chosen as the starting metric. The results show that solutions obtained from the Riccati equation and the Fourier transform are both new and different from each other.
Keywords: generating perfect fluid sphere; isotropic coordinate; modified technique; Fourier transform; ordinary differential equation;