# Hawking-Penrose Black Hole Model. Large Emission Regime

## TL;DR

This paper introduces a stochastic Markov jump process model for black hole dynamics, enabling analysis of rare large emission events through large deviation theory and identifying the most probable emission trajectories.

## Contribution

It presents a novel stochastic model of black hole quanta dynamics and applies large deviation theory to analyze rare emission events, deriving explicit rate functionals and trajectories.

## Key findings

- Derived the rate functional for large deviations in black hole emission.
- Identified the most probable trajectory for large emission events.
- Demonstrated the applicability of large deviation theory to black hole models.

## 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 components: 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 a 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 the stationarity of the fraction of quanta in the black hole, we found the most probable trajectory corresponding to a large emission event.