# Quantum Potential induced UV-IR coupling in Analogue Hawking radiation: From Bose-Einstein Condensates to canonical acoustic black holes

## TL;DR

This paper investigates how quantum potential effects in Bose-Einstein condensate-based analogue black holes induce a UV-IR coupling, affecting Hawking radiation and leading to growth of large wavelength modes.

## Contribution

It provides a detailed analysis of quantum potential induced UV-IR coupling in analogue Hawking radiation models, highlighting its impact on mode growth and experimental observations.

## Key findings

- Quantum potential causes UV-IR coupling between short and long wavelength modes.
- Large wavelength modes grow by gaining energy from Hawking radiated modes.
- Characteristic growth rates can distinguish primary and secondary modes.

## Abstract

Arising out of a Non-local non-relativistic BEC, we present an Analogue gravity model upto $\mathcal{O}(\xi^{2})$ accuracy in the presence of the quantum potential term for a canonical acoustic BH 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 in the laboratory, this UV-IR coupling is inevitable and one can not 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.