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Influence of the weakly interacting light U boson on the properties of massive PNS

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=1, we calculate and discuss the influence of U boson on the equation of state, mass-radius, moment of inertia and gravitational redshift of massive protoneutron star (PNS). The effective coupling constant $g_{U}$ of U bosons and nucleons is selected from 0GeV$^{-2}$ to 70GeV$^{-2}$. The results point that U bosons will stiffen the equation of state (EOS). The influence of U bosons on the pressure is more obvious at low density than high density, while, the influence of U bosons on the energy density is more obvious at high density than low density. The U bosons play a significant role in increasing the maximum mass and radius of PNS. When the value of $g_{U}$ changes from 0GeV$^{-2}$ to 70GeV$^{-2}$, the maximum mass of massive PNS increases from 2.11 $M_{\odot}$ to 2.58 $M_{\odot}$, and the radius of PNS corresponding PSR J0348+0432 increases from 13.71 km to 24.35 km. The U bosons will increase the moment of inertia and decrease the gravitational redshift of PNS. For PNS of the massive PSR J0348+0432, the radius and moment of inertia vary directly with $g_{U}$, the gravitational redshift vary inversely with $g_{U}$ approximately.