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The correlations of the crust-core transition density and pressure in neutronstars with the slope of the symmetry energy and the neutron skin thickness areinvestigated, using different families of relativistic mean fieldparametrizations with constant couplings and non-linear terms mixing the$\sigma$, $\omega$ and $\rho$-meson fields. It is shown that the modificationof the density dependence of the symmetry energy, involving the $\sigma$ or the$\omega$ meson, gives rise to different behaviors: the effect of the$\omega$-meson may also be reproduced within non-relativistic phenomenologicalmodels, while the effect of the $\sigma$-meson is essentially relativistic.Depending on the parametrization with $\sigma-\rho$ or $\omega-\rho$ mixingterms, different values of the slope of the symmetry energy at saturation mustbe considered in order to obtain a neutron matter equation of state compatiblewith results from chiral effective field theory. This difference leads todifferent pressures at the crust-core transition density. A linear correlationbetween the transition density and the symmetry energy slope or the neutronskin thickness of the $^{208}$Pb nucleus is obtained, only when the$\omega$-meson is used to describe the density dependence of the symmetryenergy. A comparison is made between the crust-core transition properties ofneutron stars obtained by three different methods, the Relativistic RandomPhase Approximation (RRPA), the Vlasov equation and Thermodynamical method. Itis shown that the RRPA and the Vlasov methods predict similar transitiondensities for $pne$ $\beta$-equilibrium stellar matter.

Correlation of the neutron star crust-core properties with the slope of the symmetry energy and the lead skin thickness