Anisotropic compact sphere with Van der Waals equation of state

Abstract

We formulate a system of field equations with Van der Waals type equation of state to the Einstein field equations in spherically symmetric static spacetime to describe anisotropic compact matter and obtain a new class of solution by choosing one of the gravitational potentials. The generated model is shown to be physically admissible by satisfying the major physical conditions such as regularity of gravitational potential at the origin, positive definiteness of energy density and the radial pressure at the origin, vanishing of radial pressure at some finite radius, and monotonic decrease of the energy density and the radial pressure with increasing radius. The model also satisfy the casuality condition and match smoothly with the Schwarzschild exterior line element at the stellar boundary. We believe that the solution found through this work may assist more detailed studies of relativistic compact stellar bodies at the extremes of densities.