A charged star with geometric Karmarkar condition

Abstract

In this paper, we analyse an analytical solution of the Einstein–Maxwell field equations that considers matter with anisotropic pressures in a static and spherically symmetric geometry. We report the manner in which we obtained the solution, which is by means of the Karmarkar condition. For the model, we assume a state equation that describes the interaction of matter from quarks P = (c 2 ρ − 4B g )/3 and we consider the presence of electric charge, which can generate that the radial and tangential pressures are not equal. In a graphic manner, we analyse the physical properties of the model, taking as the observational data those of mass 1M ⊙ and radius 7.69 km which were reported for the star Her X-1. The charge values are found between 5.57 × 1018C ≤ Q ≤ 1.31 × 1020C and the interval of the Bag constant B g ∈ [118.7, 122.13]MeV/fm3. Also, we show the stability of the configuration by means of the static stability criteria of Harrison–Zeldovich–Novikov , as well as in regards to infinitesimal radial adiabatic perturbation, since the adiabatic index γ > 3.3 which guarantees the stability of the solution.