Statistics of black hole radiance and the horizon area spectrum

TL;DR

This paper models black hole radiation by assuming a discrete quantum spectrum of the horizon area, deriving the statistical response and emission probabilities based on quantum jumps between area eigenstates.

Contribution

It introduces a quantum 'atomic' model of black holes with a discrete horizon area spectrum, providing a new way to calculate radiation statistics.

Findings

Derived closed-form conditional probability distribution using hypergeometric functions.

Model recovers previous radiation statistics in a quantum discrete spectrum framework.

Proposed two implementations of the quantum horizon area jump model.

Abstract

The statistical response of a Kerr black hole to incoming quantum radiation has heretofore been studied by the methods of maximum entropy or quantum field theory in curved spacetime. Neither approach pretends to take into account the quantum structure of the black hole itself. To address this last issue we calculate here the conditional probability distribution associated with the hole's response by assuming that the horizon area has a discrete quantum spectrum, and that its quantum evolution corresponds to jumps between adjacent area eigenvalues, possibly occurring in series, with consequent emission or absorption of quanta, possibly in the same mode. This "atomic" model of the black hole is implemented in two different ways and recovers the previously calculated radiation statistics in both cases. The corresponding conditional probably distribution is here expressed in closed form in terms of an hypergeometric function.