Quantum Geometry and Thermal Radiation from Black Holes
Kirill Krasnov
TL;DR
The paper investigates emission and absorption spectra of quantum black holes within a non-perturbative quantum gravity framework where horizon microstates are quantized and described by an area spectrum. It introduces an area-based canonical ensemble $p(\Gamma) \propto e^{-\tilde{\alpha} A[\Gamma]}$ and uses Fermi's golden rule to derive line intensities, linking microstate counting to thermality. A key result is that gauge invariance forbids the strongest $j=\tfrac{1}{2} \to 0$ line, while for large horizon areas the occupation numbers become area-independent with $n_j \propto j e^{-\tilde{\alpha} A_j}$, producing a Planck-like envelope $I(\omega) \propto e^{-\hbar \omega / T}$ at high frequency. The work shows how thermality emerges from a discrete quantum geometry and lays groundwork for extending the spectrum to include multi-puncture transitions and horizon fluctuations.
Abstract
A quantum mechanical description of black hole states proposed recently within non-perturbative quantum gravity is used to study the emission and absorption spectra of quantum black holes. We assume that the probability distribution of states of the quantum black hole is given by the ``area'' canonical ensemble, in which the horizon area is used instead of energy, and use Fermi's golden rule to find the line intensities. For a non-rotating black hole, we study the absorption and emission of s-waves considering a special set of emission lines. To find the line intensities we use an analogy between a microscopic state of the black hole and a state of the gas of atoms.