A regular interior solution of Einstein field equations

Abstract

Starting from the solution of the Einstein field equations in a static and spherically symmetric space–time that contains an isotropic fluid, we construct a model to represent the interior of compact objects with compactness rate [Formula: see text]. The solution is obtained by imposing the isotropy condition for the radial and tangential pressures; this generates an ordinary differential equation of second order for the temporal gtt and radial grr metric potentials, which can be solved for a specific function of gtt. The graphic analysis of the solution shows that it is physically acceptable, which is to say that the density, pressure, and speed of sound are positive, regular and monotonically decreasing functions; also, the solution is stable due to meeting the criteria of the adiabatic index. When taking the data of mass [Formula: see text] and radius [Formula: see text] that corresponds to the estimations of the star PSR J0030+045, we obtain values of central density ρc = 7.5125 × 1017 kg/m3 for the maximum compactness u = 0.19628 and of ρc = 2.8411 × 1017 kg/m3 for the minimum compactness u = 0.13460, which are consistent with those expected for this type of star.