A statistical model for constantly accelerating observers outside a Schwarzschild black hole

The statistical mechanics of black holes based on the quasi-local energy for constantly accelerating observers in the near-horizon exterior is explored. The model includes microscopic physics of both quanta of geometry, with simple quasi-local energy, and quasi-normal mode fluctuations of the horizon. The energy of geometric quanta inherits a discrete spectrum from the area quantization of loop quantum gravity. Statistics of the quanta are modeled with Bose and Fermi distributions. The model is explored in the large area limit where comparison to the Bekenstein-Hawking black hole entropy is possible. The entropy of the model is computed and the results for the entropy and the Barbero-Immirzi parameter in loop quantum gravity are discussed.