Quasi-normal modes and Microscopic Structure of the Schwarzschild Black Hole

Understand

Maggiore observed that, in the high-damping regime, the quasi-normal modes spectrum for the Schwarzschild black hole resembles that of a quantum harmonic oscillator.

• Motivated by this observation, we describe a black hole as a statistical ensemble of N quantum harmonic oscillators.
• By working in the canonical ensemble, we show that, in the large-mass black hole limit, the leading contribution to the Gibbs entropy is the Bekenstein-Hawking term, while the subleading one is a logarithmic correction, in agreement with several results in the literature.
• We also find that the number of oscillators scales holographically with the area of the event horizon.