Compact Objects from Spectral Thermodynamics and Gravitational Wave Predictions

Title: Compact Objects from Spectral Thermodynamics: Mass--Radius Relation, Kerr Emergence, and Gravitational Wave Predictions from a Single Operator Authors: Petar Iliev Dryanosvski Description: We show that the structure, stability, and gravitational wave emission of compact objects—white dwarfs, neutron stars, and black holes—emerge as distinct dynamical regimes of a single spectral entropy functional derived from a positive trace-one operator K. Key results: Tolman–Oppenheimer–Volkoff equation derived as the Euler–Lagrange equation of entropy gradient flow, not assumed as force balance Universal closed-form mass–radius relation: M(χ) = 1/(C₀ + C₁ e^{kχ}) with phase boundaries at χ = −3 (white dwarf/neutron star) and χ = 4 (neutron star/black hole), both from the stability polynomial of the spectral Hessian Numerical validation on 8 neutron stars (1.44–2.35 M⊙) confirming the three-regime structure Kerr metric emerges from ψ-sector deformation of the entropy functional; spin parameter a = J/M is the Noether charge of angular circulation Torsion-induced gravitational wave phase shift Δϕ_Ω with a specific Ω-IMR waveform template containing three parameters (α, κ, η) Hierarchical Bayesian inference: population-level detection at 3σ with ~300 events (O4); direct measurement with 10⁴–10⁵ events (ET/CE) Falsifiable: if no systematic tidal deformability bias and no coherent residual phase structure are observed at ET/CE sensitivity, the torsion sector is excluded All results follow from the spectral geometry of a single operator K. Zero free parameters. Based on: Spectral Dictionary (Zenodo: 10.5281/zenodo.20343026) and Spectral Cosmology (Zenodo: 10.5281/zenodo.20416250).