Fabbri, A., Balbinot, R., & Anderson, P. R. (2016). Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: Exact results. Phys. Rev. D, 93(6), 064046–6pp.
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 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.
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Dudley, R. A., Anderson, P. R., Balbinot, R., & Fabbri, A. (2018). Correlation patterns from massive phonons in 1+1 dimensional acoustic black holes: A toy model. Phys. Rev. D, 98(12), 124011–18pp.
Abstract: Transverse excitations in analogue black holes induce a masslike term in the longitudinal mode equation. With a simple toy model we show that correlation functions display a rather rich structure characterized by groups of approximately parallel peaks. For the most part the structure is completely different from that found in the massless case.
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Anderson, P. R., Clark, R. D., Fabbri, A., & Good, M. R. R. (2019). Late time approach to Hawking radiation: Terms beyond leading order. Phys. Rev. D, 100(6), 061703–5pp.
Abstract: Black hole evaporation is studied using wave packets for the modes. These allow for approximate frequency and time resolution. The leading order late time behavior gives the well-known Hawking radiation that is independent of how the black hole formed. The focus here is on the higher order terms and the rate at which they damp at late times. Some of these terms carry information about how the black hole formed. A general argument is given which shows that the damping is significantly slower (power law) than what might be naively expected from a stationary phase approximation (exponential). This result is verified by numerical calculations in the cases of 2D and 4D black holes that form from the collapse of a null shell.
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Balbinot, R., Fabbri, A., Dudley, R. A., & Anderson, P. R. (2019). Particle production in the interiors of acoustic black holes. Phys. Rev. D, 100(10), 105021–13pp.
Abstract: Phonon creation inside the horizons of acoustic black holes is investigated using two simple toy models. It is shown that, unlike what occurs in the exterior regions, the spectrum is not thermal. This nonthermality is due to the anomalous scattering that occurs in the interior regions.
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Dudley, R. A., Fabbri, A., Anderson, P. R., & Balbinot, R. (2020). Correlations between a Hawking particle and its partner in a 1+1D Bose-Einstein condensate analog black hole. Phys. Rev. D, 102(10), 105005–12pp.
Abstract: The Fourier transform of the density-density correlation function in a Bose-Einstein condensate (BEC) analog black hole is a useful tool to investigate correlations between the Hawking particles and their partners. It can be expressed in terms of <(out)(a) over cap (ext)(up) (out)(a) over cap (int)(up)> where (out)(a) over cap (ext)(up) is the annihilation operator for the Hawking particle and (out)(a) over cap (int)(up) is the corresponding one for the partner. This basic quantity is calculated for three different models for the BEC flow. It is shown that in each model the inclusion of the effective potential in the mode equations makes a significant difference. Furthermore, particle production induced by this effective potential in the interior of the black hole is studied for each model and shown to be nonthermal. An interesting peak that is related to the particle production and is present in some models is discussed.
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