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The emergence of the I-Love-Q relations, revealing that the moment ofinertia, the tidal Love number (deformability) and the spin-induced quadrupolemoment of compact stars are, to high accuracy, interconnected in a universalway disregarding the wide variety of equations of state (EOSs) of dense matter,has attracted much interest recently. However, the physical origin of theserelations is still a debatable issue. In the present paper, we focus on theI-Love relation for self-bound stars (SBSs) such as incompressible stars andquark stars. We formulate perturbative expansions for the moment of inertia,the tidal Love number (deformability) and the I-Love relation of SBSs. Bycomparing the respective I-Love relations of incompressible stars and aspecific kind of SBSs, we show analytically that the I-Love relation is, torelevant leading orders in stellar compactness, stationary with respect tochanges in the EOS about the incompressible limit. Hence, the universality ofthe I-Love relation is indeed attributable to the proximity of compact stars toincompressible stars, and the stationarity of the relation as unveiled here. Wealso discover that the moment of inertia and the tidal deformability of a SBSwith finite compressibility are, to leading order in compactness, equal totheir counterparts of an incompressible star with an adjusted compactness, thusleading to a novel explanation for the I-Love universal relation.

Universality and stationarity of the I-Love relation for self-bound stars