Semiclassical analysis of black holes in loop quantum gravity: Modeling Hawking radiation with volume fluctuations
Résumé
We introduce the notion of fluid approximation of a quantum spherical black hole in the context of loop quantum gravity. In this limit, the microstates of the black hole are intertwiners between “large” representations si that typically scale as si∼aH where aH denotes the area of the horizon in Planck units. The punctures with large colors are, for the black hole horizon, similar to what the fluid parcels are for a classical fluid. We dub them puncels. Hence, in the fluid limit, the horizon is composed by puncels that are themselves interpreted as composed (in the sense of the tensor product) by a large number of more fundamental intertwiners. We study the spectrum of the Euclidean volume acting on puncels and we compute its quantum fluctuations. Then, we propose an interpretation of black hole radiation based on the properties of the quantum fluctuations of the Euclidean volume operator. We estimate a typical temperature of the black hole and we show that it scales as the Hawking temperature.
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