A note on the quantization of a multi-horizon black hole

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For the motivation of focusing on the asymptotic black-hole resonances, see [ 15 ]

Cited in the paper.

These QNM resonances are valid for charged black holes that satisfy the condition e ​ Q ≳ r + / r − eQ\gtrsim r_{+}/r_{-} [this condition also reads Q / M ≳ ( ℏ / α ​ A ) 1 / 6 Q/M\gtrsim(\hbar/\alpha A)^{1/6} , where α \alpha is the fine structure constant]. For semi-classical black holes (characterized by A ≫ ℏ A\gg\hbar ) this condition is satisfied by even slightly charged black holes

Cited in the paper.

We note that the removal of classical degeneracies is actually a common feature of a quantum theory. For example, each orbital of angular momentum l l in a classical two-body system splits into 2 ​ l + 1 2l+1 distinct states in the quantum description of the hydrogen atom

Cited in the paper.

For an excellent review and a detailed list of references see H. P. Nollert, Class. Quantum Grav. 16

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This type of area quantization has since been reproduced based on various other considerations (see S. Hod, Class. Quant. Grav., 21

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2005

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