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We report an implementation of the core-valence separation approach to the 4-component relativistic Hamiltonian based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD), for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants, and the use of different Hamiltonians based on the exact 2-component (X2C) framework, on the energies of different core ionized and excited states in halogen (CH$_3$I, HX and X$^-$, X = Cl-At) and xenon containing (Xe, XeF$_2$) species. Our results show that the X2C molecular mean-field approach [Sikkema et al., J. Chem. Phys. 2009, 131, 124116], based on 4-component Dirac-Coulomb mean-field calculations ($^2$DC$^M$) is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference 4-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets yield non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine, and that the approach based on Dirac-Coulomb-Gaunt mean-field calculations ($^2$DCG$^M$) are significantly more accurate than X2C calculations for which screened two-electron spin-orbit interactions are included via atomic mean-field integrals.