A uniparametric perfect fluid solution to represent compact stars

Abstract

In the description of neutron stars, it is very important to consider gravitational theories as general relativity, due to the determining influence on the behavior of the different types of stars, since some objects show densities even bigger than nuclear density. This paper starts with Einstein’s equations for a perfect fluid and then we present a uniparametric stellar model which allows to describe compact objects like neutron stars with compactness ratio [Formula: see text]. The pressure and density are monotone decreasing regular functions, the speed of sound satisfies the causality condition, while the value for its adiabatic index [Formula: see text] guarantees the stability. In addition, the graph of [Formula: see text] versus [Formula: see text] shows a quasi-linear relationship for the equation of state [Formula: see text], which is similar to the so-called MIT Bag equation when we have the interaction between quarks. In our case it is due to the interaction of the different components found inside the star, such as electrons and neutrons. As an application of the model, we describe the star PSR J1614-2230 with a observed mass of [Formula: see text] and a radius [Formula: see text], the model shows that the maximum central density occurs for a maximal compactness value [Formula: see text].