Hawking–Penrose Black Hole Model. Large Emission Regime

Abstract

In this paper, we propose a stochastic version of the Hawking–Penrose black hole model. We describe the dynamics of the stochastic model as a continuous-time Markov jump process of quanta out and in the black hole. The average of the random process satisfies the deterministic picture accepted in the physical literature. Assuming that the number of quanta is finite the proposed Markov process consists of two componentes: the number of the quanta in the black hole and the amount of the quanta outside. The stochastic representation allows us to apply large deviation theory to study the asymptotics of probabilities of rare events when the number of quanta grows to infinity. The theory provides explicitly the rate functional for the process. Its infimum over the set of all trajectories leading to large emission event is attained on the most probable trajectory. This trajectory is a solution of a highly nonlinear Hamiltonian system of equations. Under the condition of stationarity of the fraction of quanta in the black hole, we found the most probable trajectory corresponding to a large emission event.