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 gttgtt and grrgrr, 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 (Ma=1.4M⊙(Ma=1.4M⊙, Ra=11km)Ra=11km) and (Mb=1.7M⊙(Mb=1.7M⊙, Rb=9km)Rb=9km). 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 u=GMc2Ru=GMc2R and two other parameters that characterize the internal behavior of the Hydrostatic variables, in particular the values of the central density ρcρc. In particular for the observational values of mass and radius (Ma,Ra)(Ma,Ra), we have 5.8441×1017kgm3≲ρc≲7.1755×1017kgm3 meanwhile that for (Mb,Rb) we have 1.5960×1018kgm3≲ρc≲2.0844×1018kgm3. 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.
