Quantum backreaction in an analog black hole

We extend the Gross-Pitaevskii equation to incorporate the effect of quantum fluctuations onto the flow of a weakly interacting Bose-Einstein condensate. Applying this framework to an analog black hole in a quasi- one-dimensional, transonic flow, we investigate how acoustic Hawking radiation backreacts on the background condensate. Our results point to the emergence of stationary density and velocity undulations in the supersonic region (analogous to the black-hole interior) and enable to evaluate the change in upstream and downstream Mach numbers caused by Hawking radiation. These findings provide new insight into the interplay between quantum fluctuations and analog gravity in Bose-Einstein condensates.