Semi-classical analysis of black holes in Loop Quantum Gravity: Modelling Hawking radiation with volume fluctuations

TL;DR

This paper models black hole horizons in Loop Quantum Gravity as a fluid of volume-carrying punctures, analyzing their quantum volume fluctuations to interpret Hawking radiation and estimate black hole temperature.

Contribution

It introduces a fluid approximation of quantum black hole microstates and links volume fluctuations to Hawking radiation within Loop Quantum Gravity.

Findings

Quantum volume fluctuations scale with horizon area

Estimated black hole temperature matches Hawking temperature

Horizon modeled as a fluid of punctures (puncels)

Abstract

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 $s_i$ which typically scale as $s_i \sim \sqrt{a_H}$ where $a_H$ denotes the area of the horizon in Planck units. The punctures with large colors are, for the black hole horizon, similar to what are the fluid parcels for a classical fluid. We dub them puncels. Hence, in the fluid limit, the horizon is composed by puncels which 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 holes 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.