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 spacetime 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 is 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][Formula: see text]km, from these we find that the maximum density occurs in the center for its maximum compactness.