Area spectra of the rotating BTZ black hole from quasinormal modes

Understand

Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways.

• By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit.
• According to Bohr's correspondence principle, this transition frequency at large quantum number is equal to classical oscillation frequency.
• For the corresponding classical system of periodic motion with this oscillation frequency, an action variable is identified and quantized via Bohr-Sommerfeld quantization, from which the quantized spectrum of the horizon area is obtained.