Self-amplifying Hawking radiation and its background: A numerical study

We numerically study an analog black hole with two horizons with parameters similar to a recent experiment. We find that the Hawking radiation exists on a background which contains a density oscillation, a zero-frequency ripple. The Hawking radiation evolves from spontaneous to self-amplifying, while the background ripple grows steadily with no qualitative change. It is seen that the self-amplifying Hawking radiation has a nonzero frequency. This frequency is independent of the reference frame since it is the magnitude of the wave which oscillates, as in a standing wave. The background ripple appears even before the inner horizon is created, in contrast to predictions. Furthermore, we find that technical noise and shot-to-shot variations in the number of atoms are not sufficient to cause the observed correlation function. This work is in agreement with the recent observation of self-amplifying Hawking radiation, and explains some of the features seen. In contrast to some recent works, our study differentiates between the Hawking radiation observed, and the evolution of the background.