Universality in the long-variation-length-scale limit

Establish that the universal relation among the moment of inertia, tidal deformability, and spin-induced quadrupole moment of relativistic stars is achieved when the variation length scale of the relevant physical quantities inside the star is much longer than the stellar radius.

Background

The paper investigates the proposed universality relating the dimensionless moment of inertia, tidal deformability, and spin-induced quadrupole moment of relativistic stars. Motivated by numerical experiments and analogies with universality in other areas of physics, the authors hypothesize that the relation arises from a hierarchy of length scales: the internal physical quantities governing the second-order moments should vary over scales much longer than the stellar radius.

The paper examines incompressible matter, represented by Schwarzschild's interior solution, as a possible stiff-limit candidate and finds that its second-order moments approximate those of several nuclear-theory-based equations of state. However, the authors explicitly present the long-variation-length-scale explanation as a conjecture rather than a proven result, leaving its general validity unresolved.