Quantum Black Holes and Atomic Nuclei are Hollow

TL;DR

This paper investigates quantum gravitational systems, revealing that quantum black holes and atomic nuclei can have hollow structures, with the formation depending on mass and temperature, using various quantum equations.

Contribution

It introduces solutions demonstrating hollow structures in quantum black holes and atomic nuclei through novel applications of the Schrödinger-Newton and related equations.

Findings

Quantum black holes form only above a critical mass.

Atomic nuclei are shown to be hollow structures.

Temperature influences the density distribution in quantum gases.

Abstract

The quantum Schrodinger-Newton equation is solved for a self-gravitating Bose gas at zero temperature. It is derived that the density is non-uniform and a central hollow cavity exists. The radial distribution of the particle momentum is uniform. It is shown that a quantum black hole can be formed only above a certain critical mass. The temperature effect is accounted for via the Schrodinger-Poisson-Boltzmann equation, where low and high temperature solutions are obtained. The theoretical analysis is extended to a strong interacting gas via the Schrodinger-Yukawa equation, showing that the atomic nuclei are also hollow. Hollow self-gravitating Fermi gases are described by the Thomas-Fermi equation.