Black hole lasers

High frequency dispersion does not alter the low frequency spectrum of Hawking radiation from a single black hole horizon, whether the dispersion entails subluminal or superluminal group velocities. We show here that in the presence of an inner horizon as well as an outer horizon the superluminal case differs dramatically however. The negative energy partners of Hawking quanta return to the outer horizon and stimulate more Hawking radiation if the field is bosonic or suppress it if the field is fermionic. This process leads to exponential growth or damping of the radiated flux and correlations among the quanta emitted at different times, unlike in the usual Hawking effect. These phenomena may be observable in condensed matter black hole analogues that exhibit ``superluminal'' dispersion.