CHAPTER 14: Binary Black-Hole Mergers as Hydrogen-Like Gravitational Molecules

Abstract

We develop a quantum-geometrical model of binary black-hole coalescence within the Nexus Paradigm (NP), in which black holes are represented by quantized Ricci-soliton states with eigen-radii rn = n2GM/c2. Binary configurations are formulated as coupled two-centre gravitational eigenstates whose evolution is described on an adiabatic energy surface. Applying a semiclassical orbital correspondence to the NP spectrum gives vn = c/n and fn = c3/ (πGMn3). We propose n = 2 as the lowest admissible massive terminal state of the binary sequence, yielding the zeroth-order prediction fNP 2 = c3 8πGM , which can be tested directly using independently inferred source-frame masses and gravitational-wave peak frequencies. Departures from this relation are attributed to independently calculable relativistic, finite-mass-ratio, spin-orbit and eccentricity corrections. The model possesses a semiclassical correspondence limit at n ≫ 1, whereas the strongly discrete low-n spectrum provides an additional observational test near merger. Reconciling this discreteness with smooth late-time waveforms requires sufficiently overlapping radiative transitions, providing a quantitative constraint on NP transition widths and matrix elements. The resulting framework therefore identifies two principal tests of the proposed quantum structure of black-hole coalescence: the n = 2 mass-frequency relation and possible signatures of low-n spectral discreteness in gravitational-wave signals.