From the development of Einstein´s theory of general relativity, the modelling of super dense mater configurations is an interesting research area [1,2]. In the last decades, such models allow explain the behavior of massive objects as neutron stars, quasars, pulsars, black holes and white dwarfs [3,4,5]. Malaver [3] studied the behavior of the thermal capacity C_v for Schwarzschild´s black hole when T>>T_C and T<<T_C where T_C   is the characteristic temperature of the Schwarzschild black hole and found that the value for C_v if T>>T_C is the same that would be obtained in an ideal diatomic gas if only are considered the degrees of freedom rotational. Komathiraj and Maharaj [4] find new classes exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. Sharma et al. [5] have obtained a class of solutions to the Einstein-Maxwell system assuming a particular form for the hypersurface (t=constant) containing a parameter λ .

In theoretical works of realistic stellar models, is important include the pressure anisotropy [6-8]. Bowers and Liang [6] extensively discuss the effect of pressure anisotropy in general relativity. The existence of anisotropy within a star can be explained by the presence of a solid core, phase transitions, a type III super fluid, a pion condensation [9] or another physical phenomena as the presence of an electrical field [10].    The physics of ultrahigh densities is not well understood and many of the strange stars studies have been performed within the framework of the MIT-Bag model [11]. In this model, the strange matter equation of state has a simple linear form given by where is the energy density, p is the isotropic pressure and B is the bag constant.  Many researchers have used a great variety of mathematical techniques to try to obtain exact solutions for quark stars within the framework of MIT-Bag model: Komathiraj and Maharaj [11] found two new classes of exact solutions to the Einstein-Maxwell system of equations with a particular form of the gravitational potential and isotropic pressure. Malaver [12,13] also has obtained some models for quark stars considering a potential gravitational that depends on an adjustable parameter. Thirukkanesh and Maharaj [14] studied the behavior of compact relativistic objects with anisotropic pressure in the presence of the electromagnetic field. Maharaj et al. [15] generated new models for quark stars with charged anisotropic matter considering a linear equation of state. Thirukkanesh and Ragel [16] obtained new models for compact stars with quark matter. Sunzu et al. found new classes of solutions with specific forms for the measure of anisotropy [17].  

     With then use of Einstein´s field equations, important advances have been made to model the interior of a star. Feroze and Siddiqui [18,19] considered a quadratic equation of state for the matter distribution for charged anisotropic matter. Malaver [20-24] specify particular forms for the gravitational potential and electric field intensity.  Mafa Takisa and Maharaj [25] obtained new exact solutions to the Einstein-Maxwell system of equations with a polytropic equation of state. Thirukkanesh and Ragel [26] have obtained particular models of anisotropic fluids with polytropic equation of state which are consistent with the reported experimental observations. Malaver [27,28] generated new exact solutions to the Einstein-Maxwell system considering Van der Waals modified equation of state with and without polytropical exponent and Thirukkanesh and Ragel [29] presented a anisotropic strange quark matter model by imposing a linear barotropic equation of state with Tolman IV form for the gravitational potential. Mak and Harko [30] found a relativistic model of strange quark star with the suppositions of spherical symmetry and conformal Killing vector.

The aim of this paper is to obtain new exact solutions to the Maxwell-Einstein system for charged anisotropic matter with the barotropic equation of state that presents a linear relation between the energy density and the radial pressure in static spherically symmetric spacetime using a particular form for the gravitational potential Z which depends on an adjustable parameter n. We have obtained some new classes of static spherically symmetrical models where the variation of the parameter n modifies the radial pressure, the tangential pressure, charge density and the mass of the compact objects. This article is organized as follows, in Section 2, we present Einstein´s field equations of anisotropic fluid distribution. In Section 3, we make a particular choice of gravitational potential Z(x) that allows solving the field equations and we have obtained new models for charged anisotropic matter. In Section 4, a physical analysis of the new solutions is performed. Finally, in Section 5, we conclude.

For Full Article, Please Go Through This Link: https://www.pubtexto.com/pdf/?classes-of-exact-einsteinmaxwell-solutions-with-the-mit-bag-model-equation-of-state