Stability analysis of sonic horizons in Bose-Einstein condensates

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

Sensitivity of Hawking radiation to superluminal dispersion relations

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 result

Hallazgo de terrazas pliocénicas, marinas, en la región de Llucmajor (Mallorca)

En esta nota se da a conocer, por primera vez, la presencia de depósitos Miocénicos marinos, situados en la zona meridional de la colina de Son Mulet, al Este de la villa de Llucmajor y a unos 150 m sobre el actual nivel del mar. Sus niveles de base contienen Strombus coronatus, a veces en gran cantidad. Los niveles superiores corresponden a dunas con moluscos continentales

Entropy and temperature of black holes in a gravity's rainbow

The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow.Comment: 11 pages, 2 new references added, version accepted for publication in Physical Review

Gravitational dynamics in Bose Einstein condensates

Analogue models for gravity intend to provide a framework where matter and gravity, as well as their intertwined dynamics, emerge from degrees of freedom that have a priori nothing to do with what we call gravity or matter. Bose Einstein condensates (BEC) are a natural example of analogue model since one can identify matter propagating on a (pseudo-Riemannian) metric with collective excitations above the condensate of atoms. However, until now, a description of the "analogue gravitational dynamics" for such model was missing. We show here that in a BEC system with massive quasi-particles, the gravitational dynamics can be encoded in a modified (semi-classical) Poisson equation. In particular, gravity is of extreme short range (characterized by the healing length) and the cosmological constant appears from the non-condensed fraction of atoms in the quasi-particle vacuum. While some of these features make the analogue gravitational dynamics of our BEC system quite different from standard Newtonian gravity, we nonetheless show that it can be used to draw some interesting lessons about "emergent gravity" scenarios.Comment: Replaced with published version. 15 pages, no figures, revtex4. Reference adde

The trans-Planckian problem as a guiding principle

We use the avoidance of the trans-Planckian problem of Hawking radiation as a guiding principle in searching for a compelling scenario for the evaporation of black holes or black-hole-like objects. We argue that there exist only three possible scenarios, depending on whether the classical notion of long-lived horizon is preserved by high-energy physics and on whether the dark and compact astrophysical objects that we observe have long-lived horizons in the first place. Along the way, we find that (i) a theory with high-energy superluminal signalling and a long-lived trapping horizon would be extremely unstable in astrophysical terms and that (ii) stellar pulsations of objects hovering right outside but extremely close to their gravitational radius can result in a mechanism for Hawking-like emission.Comment: 20 pages, 4 figures. v2: minor clarifications. Published versio

Cosmology as a search for overall equilibrium

In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of the cosmological constant in the equations of motion has only one weakness: The constancy of the cosmological term, or what is the same, its independence of the matter content of the universe. Eliminating this feature, I will propose what I see as a simple and reasonable modification of the cosmological equations of motion. The solutions of the new cosmological equations give place to a cosmological model that tries to approach the Einstein static solution. This model shows very appealing features in terms of fitting current observations.Comment: 9 pages, 1 figur

On asymptotically flat solutions of Einstein's equations periodic in time II. Spacetimes with scalar-field sources

We extend the work in our earlier article [4] to show that time-periodic, asymptotically-flat solutions of the Einstein equations analytic at scri, whose source is one of a range of scalar-field models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptotically-flat solutions analytic at scri, the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.Comment: 29 pages, published in Class. Quant. Grav. Replaced. Typos corrected, version which appeared in Class. Quant.Gra

Hawking Radiation on an Ion Ring in the Quantum Regime

This paper discusses a recent proposal for the simulation of acoustic black holes with ions. The ions are rotating on a ring with an inhomogeneous, but stationary velocity profile. Phonons cannot leave a region, in which the ion velocity exceeds the group velocity of the phonons, as light cannot escape from a black hole. The system is described by a discrete field theory with a nonlinear dispersion relation. Hawking radiation is emitted by this acoustic black hole, generating entanglement between the inside and the outside of the black hole. We study schemes to detect the Hawking effect in this setup.Comment: 42 pages (one column), 17 figures, published revised versio

Modelling Planck-scale Lorentz violation via analogue models

Astrophysical tests of Planck-suppressed Lorentz violations had been extensively studied in recent years and very stringent constraints have been obtained within the framework of effective field theory. There are however still some unresolved theoretical issues, in particular regarding the so called "naturalness problem" - which arises when postulating that Planck-suppressed Lorentz violations arise only from operators with mass dimension greater than four in the Lagrangian. In the work presented here we shall try to address this problem by looking at a condensed-matter analogue of the Lorentz violations considered in quantum gravity phenomenology. Specifically, we investigate the class of two-component BECs subject to laser-induced transitions between the two components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. We shall show that such a model can be considered to be an explicit example high-energy Lorentz violations where the ``naturalness problem'' does not arise.Comment: Talk given at the Fourth Meeting on Constrained Dynamics and Quantum Gravity (QG05), Cala Gonone (Sardinia, Italy) September 12-16, 200