Abstract: We investigate, within the framework of quantum field theory in curved space, the correlations across the horizon of a black hole in order to highlight the particle-partner pair creation mechanism at the origin of Hawking radiation. The analysis concerns both acoustic black holes, formed by Bose-Einstein condensates, and gravitational black holes. More precisely, we have considered a typical acoustic black hole metric with two asymptotic homogeneous regions and the Schwarzschild metric as describing a gravitational black hole. By considering equal-time correlation functions, we find a striking disagreement between the two cases: the expected characteristic peak centered along the trajectories of the Hawking particles and their partners seems to appear only for the acoustic black hole and not for the gravitational Schwarzschild one. The reason for that is the existence of a quantum atmosphere displaced from the horizon as the locus of origin of Hawking radiation together, and this is the crucial aspect, with the presence of a central singularity in the gravitational case swallowing everything is trapped inside the horizon. Correlations, however, are not absent in the gravitational case; to see them, one simply has to consider correlation functions at unequal times, which indeed display the expected peak.

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.

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.

Abstract: We consider a sonic analog of a black hole realized in the one-dimensional flow of a Bose-Einstein condensate. Our theoretical analysis demonstrates that one-and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) of the occurrence of a sonic horizon, (ii) of the associated acoustic Hawking radiation, and (iii) of the quantum nature of the Hawking process. The signature of the quantum behavior persists even at temperatures larger than the chemical potential.

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.