Charged anisotropic conformal star model with a quadratic equation of state

Abstract

A new solution to the Einstein–Maxwell field equations for a charged anisotropic compact star is generated. The presence of both a conformal Killing vector and a quadratic equation of state give rise to a new solution with astrophysical significance. The incorporation of the conformal Killing vector leads to an equation relating the gravitational potentials. By combining the quadratic equation of state with the Einstein–Maxwell field equations, an equation for electric field intensity is obtained. Subsequently, one of the gravitational potentials is chosen on physical merits to obtain the second gravitational potential and other matter variables. The generated solution undergoes a thorough analysis to ensure acceptance of physical conditions for realistic compact star models. A deep analysis of the physical aspects reveals the well-behaved nature of the gravitational potentials and matter variables. A smooth matching of the interior and exterior metrics is achieved at the boundary. The gravitational potentials are free from physical and geometric singularities. Also, the energy conditions are satisfied, and the ratio of mass to radius and the surface redshifts remain within reasonable ranges. The equilibrium is attained by the balanced natural interior physical forces. The stability of the model against gravitational collapse is satisfied. Interestingly, the use of quadratic equation of state in conformal stars is missing in treatments performed in the past.