Contraction of cold neutron star due to in the presence a quark core

Motivated by importance of the existence of quark matter on structure of neutron star. For this purpose, we use a suitable equation of state (EoS) which include three different parts: (i) a layer of hadronic matter, (ii) a mixed phase of quarks and hadrons, and, (iii) a strange quark matter in the core. For this system, in order to do more investigation of the EoS, we evaluate energy, Le Chatelier's principle and stability conditions. Our results show that the EoS satisfies these conditions. Considering this EoS, we study the effect of quark matter on the structure of neutron stars such as maximum mass and the corresponding radius, average density, compactness, Kretschmann scalar, Schwarzschild radius, gravitational redshift and dynamical stability. Also, considering the mentioned EoS in this paper, we find that the maximum mass of hybrid stars is a little smaller than that of the corresponding pure neutron star. Indeed the maximum mass of hybrid stars can be quite close to the pure neutron stars. Our calculations about the dynamical stability show that these stars are stable against the radial adiabatic infinitesimal perturbations. In addition, our analyze indicates that neutron stars are under a contraction due to the existence of quark core.