Year: 2026
Type: preprint
Abstract: We present a pedagogical introduction to the I-Love-Q relations within Newtonian gravity using an enthalpy-based formulation of stellar structure. Introducing the specific enthalpy converts Euler's equation into a first integral of hydrostatic equilibrium and recasts the equation of state as a relation between the mass density and the enthalpy. Together with Poisson's equation, these relations provide a unified description of spherical equilibrium and deformations induced by rotation and tides. We illustrate the formalism with polytropic equations of state and a relativistic free Fermi gas. In Newtonian gravity, slow uniform rotation and a weak tidal field excite the same linear quadrupolar response, yielding the exact identity $\bar I^{\,2}\bar Q/\barλ\equiv1$ for the dimensionless (``bar'') observables---independently of the equation of state. This exact identity is distinguished from the approximate universality of the pairwise I-Love-Q relations, whose residual dependence on stellar structure is illustrated by the models considered in this work.
Source: arXiv (Cornell University)
Authors: Kunjipurayil, Athul, Piekarewicz, J.
Institution: Florida State University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223673933