Exact Solutions for Charged Static Anisotropic Fluid Spheres: Physically Acceptable Models for Compact Objects

Abstract

The Einstein field equations of general relativity are solved for a static fluid sphere with charge and anisotropic pressure inclusions by adapting the isotropic uncharged Tolman VII solution to incorporate enhanced physical complexity. Physically realistic assumptions for the density and charge structure of the fluid sphere are applied to the field equations and through analytic methods, four novel exact interior solutions meeting the criteria for physical acceptability are determined. The solutions correspond to natural and self bound fluids, with two of the solutions described entirely by elementary functions and two require the use of special functions. The mathematical and physical properties of each solution are examined, which illustrates the solutions are well suited as models for compact objects. Additional properties of the solutions are explored, which include the ability to produce closed form equations of state, maximum compactness, and how potential models compare with observed compact objects.