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Anderson, P. R., Balbinot, R., Fabbri, A., & Parentani, R. (2014). Gray-body factor and infrared divergences in 1D BEC acoustic black holes. Phys. Rev. D, 90(10), 104044–6pp.
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 (omega -> 0) limit. This implies that the analog Hawking radiation is dominated by the emission of an infinite number (1/omega) of soft phonons in contrast with the case of a Schwarzschild black hole where the gray-body factor vanishes as omega -> 0 and the spectrum is not dominated by low-energy particles. The infrared behaviors of certain correlation functions are also discussed.
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Anderson, P. R., Balbinot, R., Fabbri, A., & Parentani, R. (2013). Hawking radiation correlations in Bose-Einstein condensates using quantum field theory in curved space. Phys. Rev. D, 87(12), 124018–18pp.
Abstract: The density-density correlation function is computed for the Bogoliubov pseudoparticles created in a Bose-Einstein condensate undergoing a black hole flow. On the basis of the gravitational analogy, the method used relies only on quantum field theory in curved spacetime techniques. A comparison with the results obtained by ab initio full condensed matter calculations is given, confirming the validity of the approximation used, provided the profile of the flow varies smoothly on scales compared to the condensate healing length.
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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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Anderson, P. R., Fabbri, A., & Balbinot, R. (2015). Low frequency gray-body factors and infrared divergences: Rigorous results. Phys. Rev. D, 91(6), 064061–18pp.
Abstract: Formal solutions to the mode equations for both spherically symmetric black holes and Bose-Einstein condensate acoustic black holes are obtained by writing the spatial part of the mode equation as a linear Volterra integral equation of the second kind. The solutions work for a massless minimally coupled scalar field in the s-wave or zero angular momentum sector for a spherically symmetric black hole and in the longitudinal sector of a one-dimensional Bose-Einstein condensate acoustic black hole. These solutions are used to obtain in a rigorous way analytic expressions for the scattering coefficients and gray-body factors in the zero frequency limit. They are also used to study the infrared behaviors of the symmetric two-point function and two functions derived from it: the point-split stress-energy tensor for the massless minimally coupled scalar field in Schwarzschild-de Sitter spacetime and the density-density correlation function for a Bose-Einstein condensate acoustic black hole.
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Anderson, P. R., Siahmazgi, S. G., Clark, R. D., & Fabbri, A. (2020). Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell. Phys. Rev. D, 102(12), 125035–26pp.
Abstract: A method is given to compute the stress-energy tensor for a massless minimally coupled scalar field in a spacetime where a black hole forms from the collapse of a spherically symmetric null shell in four dimensions. Part of the method involves matching the modes for the in vacuum state to a complete set of modes in Schwarzschild spacetime. The other part involves subtracting from the unrenormalized expression for the stress-energy tensor when the field is in the in vacuum state, the corresponding expression when the field is in the Unruh state and adding to this the renormalized stress-energy tensor for the field in the Unruh state. The method is shown to work in the two-dimensional case where the results are known.
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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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Carlson, E. D., Anderson, P. R., Fabbri, A., Fagnocchi, S., Hirsch, W. H., & Klyap, S. A. (2010). Semiclassical gravity in the far field limit of stars, black holes, and wormholes. Phys. Rev. D, 82(12), 124070–24pp.
Abstract: Semiclassical gravity is investigated in a large class of asymptotically flat, static, spherically symmetric spacetimes including those containing static stars, black holes, and wormholes. Specifically the stress-energy tensors of massless free spin 0 and spin 1/2 fields are computed to leading order in the asymptotic regions of these spacetimes. This is done for spin 0 fields in Schwarzschild spacetime using a WKB approximation. It is done numerically for the spin 1/2 field in Schwarzschild, extreme Reissner-Nordstrom, and various wormhole spacetimes. And it is done by finding analytic solutions to the leading order mode equations in a large class of asymptotically flat static spherically symmetric spacetimes. Agreement is shown between these various computational methods. It is found that, for all of the spacetimes considered, the energy density and pressure in the asymptotic region are proportional to r(-5) to leading order. Furthermore, for the spin 1/2 field and the conformally coupled scalar field, the stress-energy tensor depends only on the leading order geometry in the far field limit. This is also true for the minimally coupled scalar field for spacetimes containing either a static star or a black hole, but not for spacetimes containing a wormhole.
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Coutant, A., Fabbri, A., Parentani, R., Balbinot, R., & Anderson, P. R. (2012). Hawking radiation of massive modes and undulations. Phys. Rev. D, 86(6), 064022–17pp.
Abstract: We compute the analogue Hawking radiation for modes which possess a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This reflection is accompanied by an extra mode mixing which occurs in the supersonic region, and which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what is found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodynamical regime.
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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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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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