Quantum Gravitational Eigenstates in Navarro–Frenk–White Potentials

Abstract

Gravitational quantum theory applied to the weak gravity regions of deep gravitational wells predicts that photon-particle interaction cross sections can vary significantly, depending on the eigenspectral composition of the particle’s wave function. These often-reduced cross sections can potentially enable the nature and origin of dark matter to be understood without recourse to new particles or new physics, and without compromising the observations from nucleosynthesis and the cosmic microwave background. The present work extends the calculations of the Einstein-\(A\) coefficients relevant to these photon interactions (previously carried out for \(1/r\) central point-mass (CPM) potentials) to potentials derived from Navarro–Frenk–White (NFW) radial density profiles, which more realistically describe galaxy halos. The Wentzel–Kramers–Brillouin (WKB) and Modified Airy Function (MAF) approximation strategies were used to find the eigenfunctions appropriate to these potentials, and hence obtain the relevant Einstein-\(A\) coefficients. The results show that states with high principal and angular quantum number in NFW potentials have a significantly low transition rate. The results are also compared to those in the CPM potentials published in an earlier work.