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Mach's principle applied to rotation can be correct if one takes into account the rotation of the quantum vacuum together with the Universe. Whether one can detect the rotation of the vacuum or not depends on its properties. If the vacuum is fully relativistic at all scales, Mach's principle should work and one cannot distinguish the rotation: in the rotating Universe+vacuum, the co-rotating bucket will have a flat surface (not concave). However, if there are "quantum gravity" effects which violate Lorentz invariance at high energy, then the rotation will become observable. This is demonstrated by analogy in condensed-matter systems, which consist of two subsystems: superfluid background (analog of vacuum) and "relativistic" excitations (analog of matter). For the low-energy (long-wavelength) observer the rotation of the vacuum is not observable. In the rotating frame, the "relativistic" quasiparticles feel the background as a Minkowski vacuum, i.e. they do not feel the rotation. Mach's idea of the relativity of rotational motion does indeed work for them. But rotation becomes observable by high-energy observers, who can see the quantum gravity effects., Comment: 16 pages version submitted to JETP Letters

We apply a homogenization process to the acoustic velocity potential wave equation. The study of various examples shows that the resulting effective properties are different from those of the homogenized pressure wave equation for the same underlying acoustic parameters. A careful analysis reveals that a given set of inhomogeneous parameters represents an entirely different physical system depending on the considered equation. Our findings unveil a different way of tailoring acoustic properties through gradients of the static pressure. In contrast to standard metafluids based on isobaric composites, this alternative kind of metafluids is suitable for the implementation of transformational devices designed via the velocity potential equation. This includes acoustic systems in a moving background or arising from general space-time transformations. As an example, we design a device able to cloak the acoustic velocity potential., Comment: 11 pages, 4 figures

A recently developed technique known as analogue transformation acoustics has allowed the extension of the transformational paradigm to general spacetime transformations under which the acoustic equations are not form invariant. In this paper, we review the fundamentals of analogue transformation acoustics and show how this technique can be applied to build a device that increases the density of events within a given spacetime region by simultaneously compressing space and time., Comment: 17 pages 4 figures. Accepted for publication in Photon. Nanostruct. Fundam. Appl

Transformation optics has shaped up a revolutionary electromagnetic design paradigm, enabling scientists to build astonishing devices such as invisibility cloaks. Unfortunately, the application of transformation techniques to other branches of physics is often constrained by the structure of the field equations. We develop here a complete transformation method using the idea of analogue spacetimes. The method is general and could be considered as a new paradigm for controlling waves in different branches of physics, from acoustics in quantum fluids to graphene electronics. As an application, we derive an "analogue transformation acoustics" formalism that naturally allows the use of transformations mixing space and time or involving moving fluids, both of which were impossible with the standard approach. To demonstrate the power of our method, we give an explicit design of a spacetime compressor for acoustic waves and a carpet cloak for a moving aircraft., Comment: 29 pages, 11 figures, published on Scientific Reports

A recently proposed analogue transformation method has allowed the extension of transformation acoustics to general spacetime transformations. We analyze here in detail the differences between this new analogue transformation acoustics (ATA) method and the standard one (STA). We show explicitly that STA is not suitable for transformations that mix space and time. ATA takes as starting point the acoustic equation for the velocity potential, instead of that for the pressure as in STA. This velocity-potential equation by itself already allows for some transformations mixing space and time, but not all of them. We explicitly obtain the entire set of transformations that do not leave its form invariant. It is in these cases that ATA shows its true potential, allowing for building a transformation acoustics method that enables the full range of spacetime transformations. We provide an example of an important transformation which cannot be achieved with STA. Using this transformation, we design and simulate an acoustic frequency converter via the ATA approach. Furthermore, in those cases in which one can apply both the STA and ATA approaches, we study the different transformational properties of the corresponding physical quantities., Comment: 10 pages, 2 figures, published in Wave Motion 51, 785-797 (2014)

Hydrodynamic surface waves propagating on a moving background flow experience an effective curved space-time. We discuss experiments with gravity waves and capillary-gravity waves in which we study hydrodynamic black/white-hole horizons and the possibility of penetrating across them. Such possibility of penetration is due to the interaction with an additional "blue" horizon, which results from the inclusion of surface tension in the low-frequency gravity-wave theory. This interaction leads to a dispersive cusp beyond which both horizons completely disappear. We speculate the appearance of high-frequency "superluminal" corrections to be a universal characteristic of analogue gravity systems, and discuss their relevance for the trans-Planckian problem. We also discuss the role of Airy interference in hybridising the incoming waves with the flowing background (the effective spacetime) and blurring the position of the black/white-hole horizon., Comment: 29 pages. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 2011

Topological matter with Weyl points, such as superfluid 3He-A, provide an explicit example where there is a direct connection between the properly determined vacuum energy and the cosmological constant of the effective gravity emerging in condensed matter. This is in contrast to the acoustic gravity emerging in Bose-Einstein condensates, where the "value of this constant cannot be easily predicted by just looking at the ground state energy of the microscopic system from which spacetime and its dynamics should emerge" (S. Finazzi, S. Liberati and L. Sindoni, The cosmological constant: a lesson from Bose-Einstein condensates, Phys. Rev. Lett. 108, 071101 (2012)). The advantage of topological matter is that the relativistic fermions and gauge bosons emerging near the Weyl point obey the same effective metric and thus the effective gravity is more closely related to real gravity. We study this connection in the bi-metric gravity emerging in 3He-A, and its relation to the graviton masses, by comparison with a fully relativistic bi-metric theory of gravity. This shows that the parameter \lambda, which in 3He-A is the bi-metric generalization of the cosmological constant, coincides with the difference in the proper energy of the vacuum in two states (the nonequilibrium state without gravity and the equilibrium state in which gravity emerges) and is on the order of the characteristic Planck energy scale of the system. Although the cosmological constant \lambda\ is huge, the cosmological term itself is naturally non-constant and vanishes in the equilibrium vacuum, as dictated by thermodynamics. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating., Comment: 7 pages, no figures

We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time-reverse of a black hole) by measuring the angle of the Mach cone created by an object in the "supersonic" inner flow region. We emphasise the general character of this gravitational analogy by showing theoretically that the white hole horizon constitutes a stationary and spatial saddle-node bifurcation within dynamical-systems theory. We also demonstrate that the inner region has a "superluminal" dispersion relation, i.e., that the group velocity of the surface waves increases with frequency, and discuss some possible consequences with respect to the robustness of Hawking radiation. Finally, we point out that our experiment shows a concrete example of a possible "transplanckian distortion" of black/white holes., Comment: 5 pages, 5 figures. New "transplanckian effect" described. Several clarifications, additional figures and references. Published version

Fluctuations around a Bose-Einstein condensate can be described by means of Bogolubov theory leading to the notion of quasiparticle and antiquasiparticle familiar to non-relativistic condensed matter practitioners. On the other hand, we already know that these perturbations evolve according to a relativistic Klein-Gordon equation in the long wavelength approximation. For shorter wavelengths, we show that this equation acquires nontrivial corrections which modify the Klein-Gordon product. In this approach, quasiparticles can also be defined (up to the standard ambiguities due to observer-dependence). We demonstrate that---in the low as well as in the high energy regimes---both concepts of quasiparticle are actually the same, regardless of the formalism (Bogolubov or Klein-Gordon) used to describe them. These results also apply to any barotropic, inviscid, irrotational fluid, with or without quantum potential. Finally, we illustrate how the quantization of these systems of quasiparticles proceeds by analyzing a stationary configuration containing an acoustic horizon. We show that there are several possible choices of a regular vacuum state, including a regular generalization of the Boulware vacuum. Issues such us Hawking radiation crucially depend on this vacuum choice., Comment: 12 pages, 4 figures; v3: published version

Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects $E_B$ (related to the Planck scale) and the much higher scale $E_L$ signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: $E_L$ is the energy scale below which a special relativistic spacetime emerges, $E_B$ is the scale below which this spacetime geometry becomes curved. This implies that the first `quantum' gravitational effect around $E_B$ could simply be that gravity is progressively switched off, leaving an effective Minkowski quantum field theory up to much higher energies of the order of $E_L$. This scenario may have important consequences for gravitational collapse, inasmuch as it opens up new possibilities for the final state of stellar collapse other than an evaporating black hole., Comment: 6 pages, 2 figures. v2: Partially restructured; potentially observable consequence added. Several clarifications + 3 new references. To appear in Found. of Phys

An increasingly popular approach to quantum gravity rests on the idea that gravity (and maybe electromagnetism and the other gauge fields) might be an 'emergent phenomenon', in the sense of representing a collective behaviour resulting from a very different microscopic physics. A prominent example of this approach is the condensed matter scheme for quantum gravity, which considers the possibility that gravity emerges as an effective low-energy phenomenon from the quantum vacuum in a way similar to the emergence of collective excitations in condensed matter systems. This condensed matter view of the quantum vacuum clearly hints that, while the term 'ether' has been discredited for about a century, quantum gravity holds many (if not all) of the characteristics that have led people in the past to label various hypothetical substances with the term 'ether'. Since the last burst of enthusiasm for an ether, at the end of the 19th century, was brought to the grave in part by the performance of a series of important experiments in interferometry, the suggestion then naturally arises that maybe interferometry could also play a role in the current discussion on quantum gravity. We will highlight some aspects of this suggestion in the context of the condensed matter scheme for emergent gravity., Comment: 11 pages; to appear in: F. Columbus (ed.), "Interferometers: Research, Technology and Applications". v2: reference added, minor corrections

We analyze the Hawking radiation process due to collapsing configurations in the presence of superluminal modifications of the dispersion relation. With such superluminal dispersion relations, the horizon effectively becomes a frequency-dependent concept. In particular, at every moment of the collapse, there is a critical frequency above which no horizon is experienced. We show that, as a consequence, the late-time radiation suffers strong modifications, both quantitative and qualitative, compared to the standard Hawking picture. Concretely, we show that the radiation spectrum becomes dependent on the measuring time, on the surface gravities associated with different frequencies, and on the critical frequency. Even if the critical frequency is well above the Planck scale, important modifications still show up., Comment: 14 pages, 7 figures. Extensive paragraph added in conclusions to clarify obtained results

We perform a quasi-normal mode analysis of black hole configurations in Bose-Einstein condensates (BEC). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BEC with step-like discontinuities. For this case we show that in the hydrodynamic approximation quasi-normal modes do not exist. The full dispersion relation, however, allows the existence of quasi-normal modes. Remarkably, the spectrum of these modes is not discrete but continuous., Comment: 7 pages, 3 figures

We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a combination of both. We discuss the role of different boundary conditions in this stability analysis, paying special attention to their meaning in gravitational terms. We highlight that the stability of a given configuration, not only depends on its specific geometry, but especially on these boundary conditions. Under boundary conditions directly extrapolated from those in standard General Relativity, black hole configurations, white hole configurations and the combination of both into a black hole--white hole configuration are shown to be stable. However, we show that under other (less stringent) boundary conditions, configurations with a single black hole horizon remain stable, whereas white hole and black hole--white hole configurations develop instabilities associated to the presence of the sonic horizons., Comment: 14 pages, 7 figures (reduced resolution)