We generate exact solutions to the Einstein–Maxwell field equations by analysing the embedding condition. We obtain a relationship between gravitational potentials that helps to solve the embedding condition and integrate the field equations. Our choice of the measure of anisotropy and electric field are physically realistic. Our model contains several previously known solutions as special cases. These include the investigations of interior Schwarzchild metric, Finch and Skea, Hansraj and Maharaj, Feroze and Siddiqui, and Manjonjo, Maharaj andMoopanar.We also describe the structure and properties of the relativistic star by including graphical representations. Our analysis shows that the body is stable, all energy conditions are satisfied, the regularity condition is not violated, forces under equilibrium condition are balanced, all matter variables are well behaved and the matching conditions are satisfied at the boundary of the relativistic star.

We construct a new exact model for a dense stellar object utilising the Einstein–Maxwell system of equations. The model comprises three interior regions with distinct equations of state (EoS): the polytropic EoS at the core region, linear EoS at the intermediate region and Chaplygin EoS at the envelope region. Our model can regain earlier solutions. A physical analysis reveals that the matter variables, metric functions and other physical conditions are well behaved and consistent in the study of dense stellar objects. Matching of the boundary layers isdone with help of the Reissner–Nordstrom exterior space–time. An interesting feature is that the innermost region is outfitted with a polytropic EoS, and this study extends a core–envelope model developed by Mardan, Noureen and Khalid into a three-layered model.

Exact solutions to the Einstein field equations for charged relativistic anisotropic stars are generated. The Karmarkar condition is used with the Einstein–Maxwell field equations and a linear equation of state toinvestigate various physical properties and behaviour of the compact star. The nonlinear differential equations and the field equations are transformed by adopting the Bannerji and Durgapal transformation. The embedding approach provides a relationship between gravitational potentials that help to solve and integrate the field equations. This enables one to specify one of the gravitational potentials, measure of anisotropy or electric field on a physical basis.In particular, the model is generated using embedding with a linear equation of state. The detailed physical analysis of the results show that the gravitational potentials and matter variables are well behaved. The model satisfies all the necessary physical conditions, such as stability, equilibrium, energy conditions and the mass–radius relationship.