The crusts of neutron stars revisited: approximations within a polytropic equation of state approach

In this work, we revisit several thin-crust approximations presented in the literature and compare them with the exact solutions of the Tolman–Oppenheimer–Volkoff (TOV) equations. In addition, we employ three different equations of state (EoSs) and one with pasta phase, each based on a distinct framework: the variational method, relativistic Brueckner–Hartree–Fock, and relativistic mean-field theory. We emphasize that these approximations require only the TOV solutions for the core and the EoS properties at the core–crust interface, in our approach only the energy density. Finally, the relativistic approximation, as well as the Newtonian approximation with corrections, show good agreement with the exact solutions. This means that a simple treatment of the crust would suffice for structural purposes, independently of the possible uncertainties in the sub-nuclear equation of state which are not very large. The unified EOS SINPA (relativistic mean-field theory) including the pasta phase was used to study the thin-crust approximation, while degeneracy in the M M - R R relation is demonstrated through: (i) anisotropic pressure in the modified TOV equation, (ii) f(R,Lₘ,T) f ( R , L m , T ) gravity model, and (iii) dark matter admixture. As demonstrated, modifications to the description of gravitation introduce degeneracies in the mass–radius relation that are challenging to disentangle or quantify precisely.