Quantum optics meets black hole thermodynamics via conformal quantum mechanics. I. Master equation for acceleration radiation

A quantum-optics approach is used to study the nature of the acceleration radiation due to a random atomic cloud falling freely into a generalized Schwarzschild black hole through a Boulware vacuum. The properties of this horizon brightened acceleration radiation (HBAR) are analyzed with a master equation that is fully developed in a multimode format. A scheme for the coarse-graining average for an atomic cloud is considered, with emphasis on the random injection scenario, which is shown to generate a thermal state. The role played by conformal quantum mechanics (CQM) is shown to be critical for detailed balance via a Boltzmann factor governed by the near-horizon physics, with the unique selection of the Hawking temperature. The HBAR thermal state is the basis for a thermodynamic framework that parallels black hole thermodynamics.