Condensation of area quanta ensembles with quantum statistics in Schwarzschild spacetimes

As is well known, near-horizon (equivalently high acceleration) observers in spherically symmetric black hole spacetimes have a particularly simple form of the quasi-local energy. Using this energy and indistinguishable area quanta satisfying quantum statistics a statistical mechanical description of the Schwarzschild black hole geometry for uniformly accelerating observers is developed. The resulting model has several phases including one with highly excited states, Bose-Einstein condensates, condensates distinct from the usual Bose gas, and degenerate Fermi gases. In the large area limit, relevant for comparison to the Bekenstein-Hawking entropy, the new condensed state is favored over Bose-Einstein condensation and the degenerate Fermi gas. The entropies of the phases, and the entropy of mixing, are computed. The resulting low-entropic condensed state, where the quanta are essentially all in the lowest Bose energy state, provides the framework for the quantization of near-horizon geometric fluctuations, which is explored in a companion paper.