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Clement, G., & Fabbri, A. (2015). A scenario for critical scalar field collapse in AdS(3). Class. Quantum Gravity, 32(9), 095009–16pp.
Abstract: We present a family of exact solutions, depending on two parameters alpha and b (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant Lambda. For b not equal 0 these solutions reduce to the static Banados-Teitelboim-Zanelli (BTZ) family of vacuum solutions, with mass M = -alpha. For b not equal 0, the solutions become dynamical and develop a strong spacelike central singularity. The alpha < 0 solutions are black-hole like, with a global structure topologically similar to that of the BTZ black holes, and a finite effective mass. We show that the near-singularity behavior of the solutions with alpha > 0 agrees qualitatively with that observed in numerical simulations of sub-critical collapse, including the independence of the near-critical regime on the angle deficit of the spacetime. We analyze in the Lambda = 0 approximation the linear perturbations of the self-similar threshold solution, alpha = 0, and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.
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Babichev, E., & Fabbri, A. (2014). Stability analysis of black holes in massive gravity: A unified treatment. Phys. Rev. D, 89(8), 081502–5pp.
Abstract: We consider the analytic solutions of massive (bi) gravity which can be written in a simple form using advanced Eddington-Finkelstein coordinates. We analyze the stability of these solutions against radial perturbations. First we recover the previously obtained result on the instability of the bidiagonal bi-Schwarzschild solutions. In the nonbidiagonal case (which contains, in particular, the Schwarzschild solution with Minkowski fiducial metric), we show that generically there are physical spherically symmetric perturbations, but no unstable modes.
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Babichev, E., & Fabbri, A. (2014). Rotating black holes in massive gravity. Phys. Rev. D, 90(8), 084019–7pp.
Abstract: We present a solution for rotating black holes in massive gravity. We first give a solution of massive gravity with one dynamical metric. Both metrics of this solution are expressed in the advanced Eddington-Finkelstein-like coordinates: the physical metric has the original Kerr line element, while the fiducial metric is flat, but written in a rotating Eddington-Finkelstein form. For the bigravity theory we give an analogue of this solution: the two metrics have the original Kerr form, but, in general, different black hole masses. The generalization of the solution to include the electric charge is also given; it is an analogue of the Kerr-Newman solution in general relativity. We also discuss further possible ways to generalize the solutions.
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Fourdrinoy, J., Robertson, S., James, N., Fabbri, A., & Rousseaux, G. (2022). Correlations on weakly time-dependent transcritical white-hole flows. Phys. Rev. D, 105(8), 085022–14pp.
Abstract: We report observations made on a run of transcritical flows over an obstacle in a narrow channel. Downstream from the obstacle, the flows decelerate from supercritical to subcritical, typically with an undulation on the subcritical side (known in hydrodynamics as an undular hydraulic jump). In the Analogue Gravity context, this transition corresponds to a white-hole horizon. Free-surface deformations are analyzed, mainly via the two-point correlation function which shows the presence of a checkerboard pattern in the vicinity of the undulation. In nongated flows where the white-hole horizon occurs far downstream from the obstacle, this checkerboard pattern is shown to be due to low-frequency fluctuations associated with slow longitudinal movement of the undulation. Tt can thus be considered as an artifact due to a time-varying background. In gated flows, however, the undulation is typically “attached” to the obstacle, and the fluctuations associated with its movement are strongly suppressed. In this case, the observed correlation pattern is likely due to a stochastic ensemble of surface waves, scattering on a background that is essentially stationary.
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Babichev, E., & Fabbri, A. (2014). A class of charged black hole solutions in massive (bi)gravity. J. High Energy Phys., 07(7), 016–10pp.
Abstract: We present a new class of solutions describing charged black holes in massive (bi)gravity. For a generic choice of the parameters of the massive gravity action, the solution is the Reissner-Nordstrom-de Sitter metric written in the Eddington-Finkelstein coordinates for both metrics. We also study a special case of the parameters, for which the space of solutions contains an extra symmetry.
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Mauro, S., Balbinot, R., Fabbri, A., & Shapiro, I. L. (2015). Fourth derivative gravity in the auxiliary fields representation and application to the black-hole stability. Eur. Phys. J. Plus, 130(7), 135–8pp.
Abstract: We consider an auxiliary fields formulation for the general fourth-order gravity on an arbitrary curved background. The case of a Ricci-flat background is elaborated in detail and it is shown that there is an equivalence with the standard metric formulation. At the same time, using auxiliary fields helps to make perturbations to look simpler and the results clearer. As an application we reconsider the linear perturbations for the classical Schwarzschild solution. We also briefly discuss the relation to the effect of massive unphysical ghosts in the theory.
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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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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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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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Martone, G. I., Larre, P. E., Fabbri, A., & Pavloff, N. (2018). Momentum distribution and coherence of a weakly interacting Bose gas after a quench. Phys. Rev. A, 98(6), 063617–21pp.
Abstract: We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of oscillations, which are analogous to Sakharov oscillations. We identify two wide classes of time-dependent behaviors of the coupling for which an exact solution of the problem can be found, allowing for an analytic computation of all the relevant observables. A special emphasis is put on the study of the coherence property of the system in one spatial dimension. We show that the system exhibits a smooth “light-cone effect,” with typically no prethermalization.
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