Exact solutions for compact stars with CFL quark matter

Abstract

The search for the true ground state of the dense matter remains open since Bomer, Terasawa and other raised the possibility of stable quarks, boosted by Witten's strange matter hypothesis in 1984. Within this proposal, the strange matter is assumed to be composed of strange quarks in addition to the usual ups and downs, having an energy per baryon lower than the strangeless counterpart, and even lower than that of nuclear matter. In this sense, neutron stars should actually be strange stars. Later work showed that a paired, symmetric in flavor, color-flavor locked (CFL) state would be preferred to the one without any pairing for a wide range of the parameters (gap ∆, strange quark mass m s , and bag constant B). We use an approximate, yet very accurate, CFL equation of state (EoS) that generalizes the MIT bag model to obtain two families of exact solutions for the static Einstein field equations constructing families anisotropic compact relativistic objects. In this fashion, we provide exact useful solutions directly connected with microphysics.

Strange Stars Models in the Color-Flavor Locked State<strong> </strong>

“…All the obtained models are physically reasonable and satisfy the physical characteristics of a realistic star as are the regularity of the gravitational potentials at the origin, cancellation of anisotropy in r=0, radial pressure finite at the centre and decreasing of the energy density and the radial pressure from the centre to the surface of the star. These solutions match with the Schwarzschild exterior metric at the boundary for each value of adjustable parameter and the CFL phase is modelled, as it is electrically neutral according to Rocha et al [41].…”

“…In this paper, the equation of state for radial pressure is presented in the form (10) proposed by Rocha et al [41]. In eq.…”

“…In order to analytically integrate field equations, the choice of the appropriate equation of state allows obtaining models of compact stars to be physically acceptable [41]. Komathiraj and Maharaj [12], Malaver [42], Bombaci [43], Thirukkanesh and Maharaj [29], Dey et al [44] and Usov [27] assume linear equation of state for quark stars.…”

“…Malaver [46] generated new exact solutions to the Einstein-Maxwell system considering Van der Waals modified equation of state with polytropic exponent. More recently, 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.…”

“…In this paper, we generated a new class of anisotropic matter with CFL matter equation of state proposed for Rocha et al [41] in a static spherically symmetric space-time using a gravitational potential Z(x) which depends on an adjustable parameter η. We obtained some new class of static spherically symmetrical models for an uncharged anisotropic matter distribution where the variation of the parameter modifies the radial pressure, energy density, stellar radius and the mass of the compact objects.…”