True gravitational atom: Spherical cloud of dilatonic black holes

TL;DR

This paper demonstrates that an extreme dilatonic black hole can form a stable, atom-like spherical cloud of particles, with exact wave functions and spectra, opening new avenues for understanding quantum aspects of gravity.

Contribution

It is the first demonstration that an extreme dilatonic black hole can behave as a stable atom-like system with exact solutions for the surrounding particle cloud.

Findings

Exact wave functions for the particle cloud around the black hole

Spectrum of the system characterized by gravitational fine structure constant

Physical interpretation related to entropy and gravitational wave quantization

Abstract

Black hole as elementary particle is a fairly glamorous idea. For ordinary black holes, a surrounding particle inevitably penetrates into the interior of the hole since the center of the hole is an infinite potential well. For the first time we demonstrate that an extreme dilatonic black hole in spherical symmetry perfectly behaves as an atom, in the sense that its surrounding cloud of particles are completely stable. Thus we reach a spherical cloud of dilatonic black hole. We find exact wave functions of the cloud for arbitrary gravitational fine structure constant $\mu M$, and clear the underlying physical nature of the stability. Through careful studies of the exact wave function, we find the spectrum of this system. We discuss the physical meaning of this discovery especially from considerations of entropy, and the resultant possibility to explore quantization of gravitational waves from coming observations.