Gray-body factor and infrared divergences in 1D BEC acoustic black holes

Abstract

It is shown that the gray-body factor for a one-dimensional elongated Bose-Einstein condensate (BEC) acoustic black hole with one horizon does not vanish in the low-frequency ($ω\to 0$) limit. This implies that the analog Hawking radiation is dominated by the emission of an infinite number ($\frac{1}ω$) of soft phonons in contrast with the case of a Schwarzschild black hole where the gray-body factor vanishes as $ω\to 0$ and the spectrum is not dominated by low-energy particles. The infrared behaviors of certain correlation functions are also discussed.

6 pages, 2 figures. Final version. A double misprint in Eq. (21) of the published version has been corrected here