Quantum potential induced UV-IR coupling in analogue Hawking radiation: From Bose-Einstein condensates to canonical acoustic black holes

Arising out of a nonlocal nonrelativistic Bose-Einstein condensates (BEC), we present an analogue gravity model up to O(xi(2)) accuracy (xi being the healing length of the condensate) in the presence of the quantum potential term for a canonical acoustic black hole in (3 + 1)D spacetime, where the series solution of the free minimally coupled KG equation for the large-length-scale massive scalar modes is derived. We systematically address the issues of the presence of the quantum potential term being the root cause of a UV-IR coupling between short-wavelength primary modes which are supposedly Hawking-radiated through the sonic horizon and the large-wavelength secondary modes. In the quantum gravity experiments of analogue Hawking radiation within the scope of the laboratory set up, this UV-IR coupling is inevitable, and one cannot get rid of these large-wavelength excitations which would grow over space by gaining energy from the short-wavelength Hawking-radiated modes. We identify the characteristic feature in the growth rate(s) that would distinguish these primary and secondary modes.