Statistics of black hole radiance and the horizon area spectrum

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.