The Trilinear Hamiltonian: A Zero Dimensional Model of Hawking Radiation from a Quantized Source

TL;DR

This paper models Hawking radiation using a quantum parametric amplifier with a dynamical pump, revealing deviations from thermal spectra when the black hole has emitted nearly half its energy, suggesting information retention in late-time radiation.

Contribution

It introduces a zero-dimensional quantum model of Hawking radiation that accounts for the dynamical evolution of the black hole's energy and spectrum deviations from thermality.

Findings

Significant spectral deviations occur when the black hole has emitted about half its initial energy.

Late-time Hawking radiation may contain information about the black hole's quantum state.

The model supports the idea of entanglement between Hawking radiation and black hole degrees of freedom.

Abstract

We investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. The conditions are derived under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviations arise when the pump mode (black hole) has emitted nearly half of its initial energy into the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the quantum state of the black hole and is entangled with the black hole's quantum gravitational degrees of freedom.