# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1705.08249