MG11 
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Gravitating macroscopic quantum objects and their thermal properties

Thermal properties of the low temperature gravitating macroscopic quantum objects (quantum black holes) will be described. Starting with the observation that the apparent negative heat capacity for quantum systems is a finite size effect signaling a fluid-solid phase transition in the thermodynamical limit we suggest that no objects exist for which the entropy is proportional to the energy squared. The negative heat capacity of black holes following from the Bekenstein-Hawking proposal for a black hole entropy must be therefore regarded as the result of an improper classical high temperature limit of the heat capacity of a macroscopic quantum object. We show that thermal properties of selfgravitating macroscopic quantum objects are dominated by the gapless bosonic excitations which suggests a connection with physics of superfluids.