A static spherically symmetric perfect fluid solution to model the interior of stars

Abstract

An exact solution for modeling the interior of stars with perfect fluid is presented, the geometry of their interior is described by a static and spherically symmetric regular space-time. The hydrostatic functions are physically acceptable for the compactness rate u = GM/c2R ∈ (0, 0.3183497], the speed of sound is a monotonically decreasing function, positive and lower than the speed of light, which implies that the condition of causality is not violated, meanwhile the stability of the solution is guaranteed due to the adiabatic index γ > 3.08387 and it is a monotonically increasing function. The analysis of the solution is presented graphically for specific values of the compactness on the interval u ∈ [0.2509338, 0.3183497] with the minimum value of this interval associated to the neutron star PSR J0348+0432, for observational data which generates the maximum compactness when the radius is minimal R = 12.062 km and the mass is maximum M = 2.05 M¯, generating a value of the central density ρc = 7.520589 × 1017 kg/m3