Abstract
We found new classes of exact models to the Einstein-Maxwell system of equations which describe the internal structure of a compact star made of strange matter considering the equation of state proposed by Rocha, Bernardo, de Avellar and Horvath in 2019. It has been assumed that this matter is composed of equal number of up, down and strange quarks and a small amount of electrons required to reaching the charge neutrality. If this hypothesis is correct, the neutron stars would be strange stars. We have chosen a particular form of gravitational potential Z(x) that depends on an adjustable parameter related to degree of anisotropy of the models and the new solutions can be written in terms of elementary and polynomial functions. The obtained models satisfy all physical features expected in a realistic star and the expressions for mass, density and stellar radius are comparable with the experimental results.
Highlights
The analysis and description of gravitational collapse in ultracompacts objects has high importance in astrophysics and has attracted and influenced many physicists due to formulation of the general theory of relativity [1, 2]
The exact solutions as physical model of compact stars was studied by Delgaty and Lake [4] who constructed several analytical solutions that describe static spherically symmetric perfect fluid and it satisfies all the necessary conditions to be physically acceptable and interesting topic as a case research
Schwarzschild [5] found analytical solutions that allowed describing a star with uniform density, Tolman [6] developed a method to find solutions of static spheres of fluid and Oppenheimer and Volkoff [7] used Tolman's solutions to study the gravitational balance of neutron stars
Summary
The analysis and description of gravitational collapse in ultracompacts objects has high importance in astrophysics and has attracted and influenced many physicists due to formulation of the general theory of relativity [1, 2]. Many researchers and scientists have used a vast and great variety of mathematical techniques to try and test in order to obtain solutions of the Einstein-Maxwell field equations for anisotropic relativistic stars since it has been demonstrated by Komathiraj and Maharaj [28], Thirukkanesh and Maharaj [29], Maharaj et al.[30], Thirukkanesh and Ragel [31,32], Feroze and Siddiqui [33,34], Sunzu et al.[35], Pant et al [36] and Malaver [37,38,39,40] These analyses indicate that the system of Einstein-Maxwell equations is very important in the description of ultracompacts objects. Rocha et al.[41] presented a new model with anisotropic pressure and an equation of state that describes the internal structure of a compact star made of strange matter in the color flavor locked (CFL) phase This matter is assumed to be composed of equal numbers of up, down and strange quarks and a small number of electrons needed to maintain the charge neutrality.
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