An interior solution with perfect fluid and an approximated state equation P(ρ) ≈ σ(ρ −ρb)

We present a stellar model in the frame of Einstein’s general relativity considering a static and spherically symmetric space time which contains a perfect fluid. The analytical solution is determined starting from a temporal metric function that facilitates the integration of the system. We show that the state equation associated to the model can be approximated in the form Formula: see text, where Formula: see text is the density on the surface of the star. The stability under adiabatic and radial perturbations of static, compact stellar objects with sources of matter from a perfect fluid will determine the maximum value of compactness Formula: see text, the model also results to be stable according to the criteria of Harrison - Zeldovich - Novikov. In a complementary manner the model is verified for the observational data of the compact object XMMU J173203.3-344518 in HESS J1731-347, of low mass Formula: see text and radius Formula: see text km, from these we find that the maximum density occurs in the center for its maximum compactness.