1112.3596 (Massimiliano Rinaldi)

The entropy of an acoustic black hole in Bose-Einstein condensates:
higher order corrections and infrared divergences    [PDF]

Massimiliano Rinaldi

We consider the entropy associated to the phonons generated via the Hawking mechanism in a sonic hole in a Bose-Einsten condensate. In a previous paper, we looked at the (1+1)-dimensional case both in the hydrodynamic limit and in the case when high-frequency dispersion is taken in account \cite{acentropy}. Here, we extend the analysis by including transverse excitations, and show that they can cure the infrared divergence that appeared in the (1+1)-dimensional case. We also compute higher order corrections to the entropy in the hydrodynamic limit, and we find that these suffer from the same ultraviolet divergences that affect the leading order. On the contrary, the transverse modes have a much stronger effect in the dispersive case, as the entropy not only is finite, but it turns out to be equal to just 1/6, with small corrections that depend on the wavelength of the transverse modes.

View original: http://arxiv.org/abs/1112.3596