Relativistic theory of di-Holeums - quantized gravitational bound states of two micro black holes

Abstract

The Klein-Gordon equation is solved for di-Holeums (gravitational bound states of two micro black holes) for scalar and vector gravity in its static limit. The relativistic models confirm the predictions of the nonrelativistic Newtonian gravity model, correct to about six significant figures over almost the entire sub-Planck domain. All three models possess a mass range devoid of physics. This is interpreted as evidence that the universe must have more than four dimensions. We show that the formation of Holeums is feasible both in the sub-Planck mass and above-Planck mass ranges.