Microscopic Black Hole Pairs in Highly-Excited States

TL;DR

This paper explores the quantum behavior of a pair of microscopic black holes in highly excited states, revealing discrete energy levels, rapid transitions, and extremely energetic graviton emissions.

Contribution

It introduces a quantum mechanical model of two Planck-scale black holes, showing their energy spectrum and transition dynamics in highly excited states.

Findings

Discrete energy eigenstates exist even at high excitation levels.

Transitions between states occur rapidly, on the order of 10^{-30} seconds.

Gravitons emitted have energies around 10^{22} eV.

Abstract

We consider the quantum mechanics of a system consisting of two identical, Planck-size Schwarzschild black holes revolving around their common center of mass. We find that even in a very highly-excited state such a system has very sharp, discrete energy eigenstates, and the system performs very rapid transitions from a one stationary state to another. For instance, when the system is in the 100th excited state, the life times of the energy eigenstates are of the order of $10^{-30}$ s, and the energies of gravitons released in transitions between nearby states are of the order of $10^{22}$ eV.