Black hole lasers revisited

The production of Hawking radiation by a single horizon is not dependent on the high-frequency dispersion relation of the radiated field. When there are two horizons, however, Corley and Jacobson have shown that superluminal dispersion leads to an amplification of the particle production in the case of bosons. The analytic theory of this "black hole laser" process is quite complicated, so we provide some numerical results in the hope of aiding understanding of this interesting phenomenon. Specifically, we consider sonic horizons in a moving fluid. The theory of elementary excitations in a Bose-Einstein condensate provides an example of "superluminal" (Bogoliubov) dispersion, so we add Bogoliubov dispersion to Unruh's equation for sound in the fluid. A white-hole/black-hole horizon pair will then display black hole lasing. Numerical analysis of the evolution of a wave packet gives a clear picture of the amplification process. By utilizing the similarity of a radiating horizon to a parametric amplifier in quantum optics we also analyze the black hole laser as a quantum-optical network.