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We suggest a quantum black hole model that is based on an analogue to hydrogen atoms. A self-regular Schwarzschild-AdS black hole is investigated, where the mass density of the extreme black hole is given by the probability density of the ground state of hydrogen atoms and the mass densities of nonextreme black holes are given by the probability densities of excited states with no angular momenta. Such an analogue is inclined to adopt quantization of black hole horizons. In this way, the total mass of black holes is quantized. Furthermore, the quantum hoop conjecture and the Correspondence Principle are discussed.

It has been desirable that a nonperturbative quantum gravity theory should have no ultraviolet (UV) divergences [

The idea of the self-completeness mentioned above has been realized by Nicolini et al. [

Based on such a modification of mass distribution mentioned above, a new self-regular quantum black hole proposal [

Inspired by the interesting Bohr-like quantization [

The arrangement of this paper is as follows. In Section

The metric of the static and spherically symmetric self-regular Schwarzschild-AdS black hole, where the noncommutativity of spacetime has been considered, takes the form

We emphasize that the metric solution (

According to our proposal, we take the probability density of the ground state of a hydrogen atom,

Substituting (

The blue curve corresponds to the relation equation (

We can observe in Figure

By requiring

The numerical points of (

We now analyze the

If

In order to ensure the formation of a black hole, the hoop conjecture should be considered; that is, the mean radius of a black hole related to some mass distribution should not be larger than the horizon radius of the relevant extreme black hole. The mean radius for the mass density equation (

As a result, when the

In accordance with our proposal mentioned in Section

Substituting (

In [

We plot (

Plots of the relations between black hole masses and their horizon radii. The blue, red, orange, and green curves correspond to the cases of

Now we turn to the discussion of the quantum hoop conjecture which has the following form [

As to the Correspondence Principle, it usually indicates a transition from quantum theory to classical theory. In quantum mechanics, there are two alternatives to realize such a transition. One is the limit of a large quantum number, and the other is the limit of

Based on the recent works by Corda [

The authors declare that they have no competing interests.

Chang Liu would like to thank X. Hao and L. Zhao of Nankai University for their helpful discussions. Yan-Gang Miao would like to thank W. Lerche of PH-TH Division of CERN for kind hospitality. This work was supported in part by the National Natural Science Foundation of China under Grant no. 11175090 and by the Ministry of Education of China under Grant no. 20120031110027.