Regularization of fluctuations near the sonic horizon due to the quantum potential and its influence on the Hawking radiation

TL;DR

This paper investigates how quantum potential regularizes fluctuations near the sonic horizon in Bose-Einstein condensates and nonlinear optical media, affecting the characteristics of Hawking radiation spectra.

Contribution

It introduces a second characteristic length scale that regularizes fluctuations near the sonic horizon when quantum potential is considered, altering the Hawking radiation spectrum.

Findings

Existence of a second length scale $l_r$ for regularization

Quantum potential influences high-frequency tail of Hawking radiation

Fluctuation modes become regularized near the sonic horizon

Abstract

We consider dynamics of fluctuations in transonically accelerating Bose-Einstein condensates and luminous liquids (coherent light propagating in a Kerr nonlinear medium) using the hydrodynamic approach. It is known that neglecting the quantum potential (QP) leads to a singular behavior of quantum and classical fluctuations in the vicinity of the Mach (sonic) horizon, which in turn gives rise to the Hawking radiation. The neglect of QP is well founded at not too small distances $|x| \gg l_h$ from the horizon, where $l_h$ is the healing length. Taking the QP into account we show that a second characteristic length $l_r > l_h$ exists, such that the linear fluctuation modes become regularized for $|x| \ll l_r$. At $|x| \gg l_r$ the modes keep their singular behavior, which however is influenced by the QP. As a result we find a deviation of the high frequency tail of the spectrum of Hawking radiation from Planck's black body radiation distribution. Similar results hold for the wave propagation in Kerr nonlinear media where the length $l_h$ and $l_r$ exist due to the nonlinearity.