Bose condensation and the BTZ black hole

Abstract

Although all popular approaches to quantum gravity are able to recover the BekensteinHawking 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 Bañados-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.

Condensation of an ideal gas with intermediate statistics on the horizon

“…This condensed state represents a kind of brick-wall model and can be used to count horizon degrees of freedom. This finding is in certain ways similar to those of a recent study about condensation and BTZ black holes [52]. In a recent paper Dvali and Gomez (DG) [53] proposed that black holes are nothing but a Bose-Einstein condensate of gravitons.…”

Quantum dust collapse in 2+1 dimensions

“…which automatically obeys the momentum constraint provided W doesn't have any explicit dependence on r. At this point we will consider a one-dimensional lattice with discrete points r i , a distance σ apart. With this discretization and the ansatz in (12) the WDW equation gives…”