Bose Condensation and the BTZ Black Hole

Although all popular approaches to quantum gravity are able to recover the Bekenstein-Hawking entropy-area law in the thermodynamic limit, there are significant differences in their descriptions of the microstates and in the application of statistics. Therefore they can have significantly different phenomenological implications. For example, requiring indistinguishability of the elementary degrees of freedom should lead to changes in the black hole's radiative porperties away from the thermodynamic limit and at low temperatures. We demonstrate this for the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. The energy eigenstates and statistical entropy in the thermodynamic limit of the BTZ black hole were obtained earlier by us via symmetry reduced canonical quantum gravity. In that model the BTZ black hole behaves as a system of Bosonic mass shells moving in a one dimensional harmonic trap. Bose condensation does not occur in the thermodynamic limit but this system possesses a finite critical temperature, $T_c$, and exhibits a large condensate fraction below $T_c$ when the number of shells is finite.Comment: 5 pages, 5 figures. Published versio