Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: Exact results

Abstract

A complete set of exact analytic solutions to the mode equation is found in the region exterior to the acoustic horizon for a class of 1D Bose-Einstein condensate (BEC) acoustic black holes. From these, analytic expressions for the scattering coefficients and gray-body factor are obtained. The results are used to verify previous predictions regarding the behaviors of the scattering coefficients and gray-body factor in the low frequency limit. * afabbri@ific.uv.es † Roberto.Balbinot@bo.infn.it ‡ anderson@wfu.edu 2

Low-frequency analogue Hawking radiation: The Bogoliubov-de Gennes model

“…Although this is presumably difficult to set experimentally, this case is interesting for its mathematical simplicity. For this reason, it has been previously studied in details in the phononic regime [13][14][15] and in the step regime [11,44]. Our method allows us to generalize these results for any value of the transition size L compared to the healing length ξ.…”

“…[9] for more details). The sign in equation (15), is the sign of the norm of the corresponding mode. It indicates if that mode is associated with a creation or annihilation operator [9,25].…”

“…In this work, we study the low-frequency properties of the Hawking effect, and demonstrate that the spectrum increases at low frequencies in the most general case. We consider both greybody factors and the effect of dispersion (not considered in [13][14][15]). For this, we use a generalization of the matched asymptotic expansion method [16,17], that allows us to fully characterize the scattering at low frequencies.…”

“…A particular consequence of these greybody factors is that the low-frequency emission spectrum of a black hole is suppressed, because low-frequency modes do not have enough energy to escape from the gravitational potential. On the contrary, in one-dimensional acoustic flows, it was discovered that the spectrum of the Hawking effect is dominant at low frequencies [9,[11][12][13][14][15].…”

Low-frequency analogue Hawking radiation: The Korteweg–de Vries model

“…There is in principle another source of deviation which affects the thermality of the black hole spectra in an analogue gravity system. This other source is greybody factors, which are expected to occur in both analogue [19][20][21] and astrophysical [22] black holes. Greybody factors account for the partial reflection of the Hawking radiation propagating away from the horizon back into the black hole.…”