Neutron star under homotopy perturbation method

We obtain a mass function solving the Tolman-Oppenheimer-Volkoff (TOV) equation for isotropic and spherically symmetric system via homotopy perturbation method (HPM). Using the mass function we construct a stellar model which can be determined from the equation of state (EOS) parameter ($\omega$) and a model parameter ($n$). With the help of Einstein field equations we develop three solutions which can describe different properties and the core-crust structure of neutron star (NS). Solution I is valid for NS having the inner and outer radius near the surface of the star. The star is physical up to the inner radius whereas negative density occurs and the energy conditions are violated in the upper region from the inner to outer radius. Solution II represents NS with high gravitational redshift as well as compactification factor. All the features of NS can be given by solution III which involves only the EOS parameter. Our model predicts maximum mass for a NS with the central density $5.5\times10^{15}~g/cm^{3}$ and surface redshift 0.69 is to be $2.01~M_\odot$ for the EOS parameter $\omega=0.73$. The predicted range for the surface redshift is $0.57<Z_s<1.95$ for the allowed ranges $8.4<n<10.9$ and $1/3<\omega<1$ in the presented NS model.