Quantum Electron Clouds near Black Holes: Black Atoms and Molecules

We study quantum mechanical wavefunctions near highly curved spaces, i.e., black holes. By utilizing the formalism developed by DeWitt, we derive the Schrödinger equations in the vicinity of the Schwarzschild and the Reissner-Nordström black hole geometries. The quantum electron cloud for the “black hydrogen atom” - an electron trapped by black holes - is particularly studied. We solve the equations and find that black holes generally attract the wavefunctions, localizing them near the horizon where the electrons are most likely to be trapped. These results imply that not only classical objects but also the quantum material and even the chemical properties of the atoms are affected by strong gravity. We also discuss black hydrogen molecules composed of multi-centered Majumdar-Papapetrou black holes.

💡 Research Summary

The paper “Quantum Electron Clouds near Black Holes: Black Atoms and Molecules” investigates how strong gravitational fields affect quantum‑mechanical wavefunctions on atomic scales. Using the DeWitt formalism for quantum mechanics in curved configuration spaces, the authors derive a non‑relativistic Schrödinger equation that incorporates the spatial metric g_{ij} and its curvature through an additional term ℏ²R^{(3)}/12 in the Hamiltonian. They first apply this formalism to the Schwarzschild black hole. Starting from the Cartesian metric, they perform a canonical quantization, then transform to spherical coordinates to obtain a radial equation

(1‑a/r)R’’ + (2/r‑3a/r²)R’ +