A regular interior solution of Einstein field equations

Abstract

Starting from the solution of the Einstein field equations in a static and spherically symmetric spacetime which contains an isotropic fluid, we construct a model to represent the interior of compact objects with compactness rate $u=\frac{GM}{c^2R}<0.23577$. 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 $g_{tt}$ and radial $g_{rr}$ metric potentials, which can be solved for a specific function of $g_{tt}$. The graphic analysis of the solution shows that it is physically acceptable, that is to say, 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 $M=1.44^{+0.15}_{-0.14}M_\odot$ and radius $R=13.02^{+1.24}_{-1.06}km$ which corresponds to the estimations of the star PSR J0030+045 we obtain values of central density $\rho_c=7.5125\times 10^{17} kg/m^3$ for the maximum compactness $u=0.19628$ and of $\rho_c= 2.8411 \times 10^{17} kg/m^3$ for the minimum compactness $u=0.13460$, which are consistent with those expected for this type of stars.