We generate two newexact models for the Einstein–Maxwell field equations. In our models, we consider the stellar object that is anisotropic and charged with linear equation of state consistent with quark stars. We have a new choice of measure of anisotropy that is physically reasonable. It is interesting that in our models we regain previous isotropic results as special cases. Isotropic exact solutions regained include models by Komathiraj and Maharaj; Mak and Harko; and Misner and Zapolsky. We can also obtain particular anisotropic models obtained by Maharaj, Sunzu, and Ray. The exact solutions corresponding to our models are found explicitly in terms of elementary functions. The graphical plots generated for the matter variables and the electric field are well behaved. We also generate relativistic stellar masses consistent with observations.

We obtain new regular exact solutions to the field equations for uncharged relativistic stellar objects with vanishing pressure anisotropy. We assume a quadratic equation of state and a choice of measure of anisotropy and a metric function defining one of the gravitational potentials. In our exact models, we regain anisotropic and isotropic results generated by other researchers as a special case. It is interesting that our results are in agreement withMinkowski space–time and earlier Einstein models. The physical analysis of the plots reveals that the gravitational potentials and matter variables are well behaved in the stellar interior. Using our model, we generate finite relativistic stellar masses which are consistent with the astronomical objects previously found by other researchers.

We find new stellar models to the field equations for charged anisotropic spheres. We use linear quarkequation of state for strange quarkmatter.We choose a new form of pressure anisotropy as a rational function. In ourmodel, we regain previous isotropic and anisotropic stellar models as specific cases. Isotropic models regained arethose found by Komathiraj and Maharaj, Mak and Harko, and Misner and Zapolsky. Anisotropic models regainedinclude the performance by Maharaj, Sunzu and Ray; and Sunzu and Danford. We indicate that our model meetsthe stability and energy conditions. We also generate stellar masses consistent with observations.

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.

A new regular model for a stellar sphere with quark matter is found. The model satisfies a neutral quark star with pressure anisotropy. In this model, we consider an ansatz of a new form of one of the gravitational potentials, and stellar masses consistent with other findings which describe the generation of astrophysical objects. New masses, radii and surface gravitational red-shifts in acceptable ranges are also obtained using our model. The model satisfies stability and energy conditions. The state of hydrostatic equilibrium for stability is obtained by analysing the Tolman–Oppenheimer–Volkoff (TOV) equation. All other matter variables and gravitational potentialsare well behaved.

New models for the charged anisotropic stellar object were generated using the Einstein–Maxwell field equations. A new choice of pressure anisotropy in logarithmic form was used to generate a quark star model. Anisotropic and isotropic models were regained as a special case.We regained anisotropic models found by Maharaj, Sunzu and Ray; Abdalla, Sunzu and Mkenyeleye; and Sunzu and Danford. The isotropic models regained include the performance by Mak and Harko, and Maharaj and Komathiraj. Physical analysis showed that matter variables and the gravitational potentials are well behaved. Our model does satisfy the energy conditions and stability condition.

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.