Tidal Deformability of Neutron Stars in Recursive Dimensionality Theory: Gravitational Wave Signatures and Universal Relations

This paper extends Recursive Dimensionality Theory (RDT) to the tidal deformability of neutron stars and its observable impact on gravitational-wave signals from binary neutron star mergers. RDT proposes that the effective spatial dimensionality of matter varies slowly with density, introducing controlled geometric modifications to relativistic stellar structure without altering the underlying equations of general relativity in vacuum.

Using standard tidal perturbation methods applied to RDT-modified stellar backgrounds, we compute tidal Love numbers and dimensionless tidal deformabilities for realistic equations of state. We find that RDT generically increases tidal deformability by tens of percent in a mass-dependent manner, while preserving established universal relations such as the I–Love relation. These effects are largely independent of the choice of equation of state and arise primarily from geometric radius scaling, with smaller contributions from changes in the internal response.

The resulting signatures are directly testable with current and next-generation gravitational-wave detectors and provide a clean observational pathway for constraining or falsifying RDT using compact-object mergers.

Version 2

A sign error in the stated dimensional law has been corrected in this version: the effective dimensionality decreases logarithmically with density above the reference scale. All numerical results are unchanged, as the implementation already used the correct form.