Generating Theorems for Charged Anisotropy in General Relativity

Abstract

For describing the interior of a spherical object in the general relativistic frame, some objects can be considered using the concept of perfect fluid spheres for simplicity. The absence of heat conduction and shear stress, and the presence of isotropic pressure are the characteristics of perfect fluid spheres. Previous works in this field constitute finding solutions for perfect fluid spheres in various coordinates. In this work, we are interested in generating anisotropic solution for fluid spheres. The particular property of anisotropy, which differs from the property of perfect fluid spheres, is that the radial pressure and the transverse pressure are not equal. One cause of anisotropy is the presence of charge inside an object. Anisotropic fluid spheres are models for describing a charged star such as a neutron star. An important tool in studying fluid sphere solutions is the solution generating algorithm. This technique can be used to generate new solution from known solutions without having to solve Einstein’s equation directly. The solution generating theorems for anisotropic fluid spheres are constructed in terms of the metric of spacetime. The other purpose is to classify the types of solution into seed and non-seed metrices.