Limiting cases of second-order moments of relativistic stars and their universality

Abstract

Extending the work presented in a workshop ``From Quarks to Neutron Stars: Insights from kHz gravitational waves'', we discuss some limiting cases of the moment of inertia, tidal deformability, and spin-induced quadrupole moment for relativistic stars. First, conjecturing that a hierarchy of the length scale is the key to proposed universality among these second-order moments, we revisit the relation for incompressible relativistic stars (known as Schwarzschild's interior solution) as a candidate of the possible stiff limit. Second, we present the limiting form for the weak-field limit. In particular, we demonstrate how relativistic computations of tidal deformation are related to the traditional Newtonian counterpart, which might not have been presented explicitly in the literature.