An interior solution with perfect fluid
Abstract
Starting from the construction of a solution for Einstein’s equations with a perfect fluid for a static spherically symmetric spacetime, we present a model for stars with a compactness rate of u≤0.114508. The model is physically acceptable, that is to say, its geometry is non-singular and does not have an event horizon, pressure and speed of sound are bounded functions, positive and monotonically decreasing as function of the radial coordinate, also the speed of sound is lower than the speed of light. While it is shown that the adiabatic index γ>14.615, which guarantees the stability of the solution. In a complementary manner, numerical data are presented considering the star PSR J0737-3039A with observational mass of 1.3381M⊙, for the value of compactness 0.105395, which implies the radius R=18745.32m and the range of the density ρb=0.931561×1017kg/m3≤ρ≤1.012207×1017kg/m3=ρc, where ρc and ρb are the central density and the surface density, respectively. This range is consistent with the expected values; as such, the model presented allows to describe this type of stars.
