A note on hierarchy of universal relations for neutron stars in terms of multipole moments

Recent studies of the analytical and numerical models of neutron stars suggest that their exterior field can be well approximated by only four arbitrary parameters of the 2-soliton solution of Einstein's equations, which gives rise to the so-called no-hair conjecture for neutron stars proposed by Yagi et al. By assuming that the latter conjecture is correct, we show that there exists an infinite hierarchy of universal relations for neutron stars in terms of multipole moments that arises as a series of the degeneration conditions for generic soliton solutions. The analysis of the simplest of these relations involving the hexadecapole mass moment is able to reveal which of the known equations of state for the stellar interior are most consistent with the Yagi et al conjecture.