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This study provides a pedagogical examination of the I-Love-Q relations in Newtonian gravity using an enthalpy-based approach to stellar structure. The authors demonstrate that in Newtonian gravity, slow rotation and weak tidal fields produce identical quadrupolar responses, yielding an exact mathematical identity relating moment of inertia (I), tidal deformability (Love number), and quadrupole moment (Q). This exact relation is contrasted with the approximate universal I-Love-Q relations, whose small variations depend on the specific stellar equation of state.
Why it matters
These relations are important for interpreting observations of neutron stars and other compact objects, particularly through gravitational wave astronomy. Understanding which aspects of I-Love-Q relations are exact versus approximate helps constrain neutron star properties and equations of state from observational data.
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⚠️ Preprint – Noch nicht peer-reviewed
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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 $bar I^{,2}bar Q/barlambdaequiv1$ 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: Newtonian I-Love-Q relations: An enthalpy-based approach