A simple geometry to model fluid spheres in general relativity

Abstract

A simple geometry which is static and spherically symmetrical is proposed, useful to model a fluid sphere in general relativity. This allows us to describe the interior of stellar objects both neutral and charged. It is shown that in both cases the solution is stable, which means that the behavior of the density and radial pressure is monotonic decreasing functions. Both models depend on two parameters, in the neutral case, these are the compactness rate $u=GM/c^2R$ and w related to the monotonically increasing or decreasing behavior of the speed of sound, and in the charged case, they are the compactness rate and the rate between the charge Q and the radius R, $q=Q/R$. A comparison is done between the case of a charged perfect fluid and the case of an anisotropic fluid; from there we can show that, as a result of the presence of the charge and its repulsion effect that it generates at a local and universal level, the density for the anisotropic case is greater than the density in the charged case. For both models, we obtain physical values of objects with a compactness rate $u=0.35578$ for the particular cases of masses and radios for $(M_\odot ,R=4150.1\,\mathrm{m})$, $(1.5M_\odot ,R=6225\,\mathrm{m})$, $(2M_\odot ,R=8300 m)$. In the neutral case, the greater central density $\rho _c=5.0840\times 10^{19} \,\mathrm{kg/m}^3$ matches the object of $1.5M_\odot$ and for the charged case, the maximum central density is of $\rho _c=8.8439\times 10^{18} \,\mathrm{kg/m}^3$, associated with the star with $1M_\odot$. Additionally, by using the proposed model, we obtain the values of density and pressure for the star PSR J1614–223, the maximum value of the central density $\rho _c=1.0573\times 10^{18} \,\mathrm{kg/m}^3$.