Description of the interior of the neutron star in EXO 1785-248 by mean of the Karmarkar condition

Abstract

Starting from the known condition of Karmarkar, which guarantees that a static and spherically symmetrical space-time is embedded in a manifold of dimension 5, and that it generates a differential equation between the metric coefficients [Formula: see text] and [Formula: see text], we solve Einstein’s equations for a fluid with anisotropic pressures. This allows us to represent the interior of the neutron star EXO 1785-248, with observational data around the pair of mass and radius [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text]. It is shown that the density, radial and tangential pressure are monotonically decreasing functions, while the radial and tangential speeds of sound satisfy the causality conditions. The model presented depends on the compactness [Formula: see text] and two other parameters that characterize the internal behavior of the Hydrostatic variables, in particular the values of the central density [Formula: see text]. In particular for the observational values of mass and radius [Formula: see text], we have [Formula: see text] meanwhile that for [Formula: see text] we have [Formula: see text]. In a complementary manner it is shown that the model satisfies the causality condition and that according to the stability criteria of Harrison–Zeldovich–Novikov and of cracking the solution is stable.

A charged star with geometric Karmarkar condition

“…that was previously proposed in the description of solutions with anisotropic fluid [73] and for a perfect charged fluid [74].…”