Quantum Non-Gravity and Stellar Collapse

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 Phy

Quasi-normal mode analysis in BEC acoustic black holes

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 figure

The Discrete Fundamental Group of the Associahedron, and the Exchange Module

The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras. We approach the associahedron from the point of view of discrete homotopy theory. We study the abelianization of the discrete fundamental group, and show that it is free abelian of rank $\binom{n+2}{4}$. We also find a combinatorial description for a basis of this rank. We also introduce the exchange module of the type $A_n$ cluster algebra, used to model the relations in the cluster algebra. We use the discrete fundamental group to the study of exchange module, and show that it is also free abelian of rank $\binom{n+2}{3}$.Comment: 16 pages, 4 figure

On the robustness of acoustic black hole spectra

We study the robustness of the spectrum emitted by an acoustic black hole by considering series of stationary flows that become either subsonic or supersonic, i.e. when the horizon disappears. We work with the superluminal Bogoliubov dispersion of Bose--Einstein condensates. We find that the spectrum remains remarkably Planckian until the horizon disappears. When the flow is everywhere supersonic, new pair creation channels open. This will be the subject of a forthcoming work.Comment: 4 pages, 2 figure, jpconf.cls; to appear in the proceedings of the Spanish Relativity Meeting ERE201

Editorial of special issue “the interplay of microbiome and immune response in health and diseases”

Increasing data suggests and supports the idea that the gut microbiota (GM) modulates different host pathways, playing a crucial role in human physiology and consequently impacting in the development of some pathologic conditions [...

Acoustic horizons for axially and spherically symmetric fluid flow

We investigate the formation of acoustic horizons for an inviscid fluid moving in a pipe in the case of stationary and axi-symmetric flow. We show that, differently from what is generally believed, the acoustic horizon forms in correspondence of either a local minimum or maximum of the flux tube cross-section. Similarly, the external potential is required to have either a maximum or a minimum at the horizon, so that the external force has to vanish there. Choosing a power-law equation of state for the fluid, $P\propto \rho^{n}$, we solve the equations of the fluid dynamics and show that the two possibilities are realized respectively for $n>-1$ and $n<-1$. These results are extended also to the case of spherically symmetric flow.Comment: 6 pages, 3 figure

About Locality and the Relativity Principle Beyond Special Relativity

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality \cite{AmelinoCamelia:2011bm} has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-called Doubly Special Relativity theories.Comment: 10 pages, no figure

Noether Current, Horizon Virasoro Algebra and Entropy

We provide a simple and straightforward procedure for defining a Virasoro algebra based on the diffeomorphisms near a null surface in a spacetime and obtain the entropy density of the null surface from its central charge. We use the off-shell Noether current corresponding to the diffeomorphism invariance of a gravitational Lagrangian $L(g_{ab},R_{abcd})$ and define the Virasoro algebra from its variation. This allows us to identify the central charge and the zero mode eigenvalue using which we obtain the entropy density of the Killing horizon. Our approach works for all Lanczos-Lovelock models and reproduces the correct Wald entropy. The entire analysis is done off-shell without using the field equations and allows us to define an entropy density for any null surface which acts as a local Rindler horizon for a particular class of observers.Comment: V2: to appear in Phys. Rev.

Emergent Horizons in the Laboratory

The concept of a horizon known from general relativity describes the loss of causal connection and can be applied to non-gravitational scenarios such as out-of-equilibrium condensed-matter systems in the laboratory. This analogy facilitates the identification and theoretical study (e.g., regarding the trans-Planckian problem) and possibly the experimental verification of "exotic" effects known from gravity and cosmology, such as Hawking radiation. Furthermore, it yields a unified description and better understanding of non-equilibrium phenomena in condensed matter systems and their universal features. By means of several examples including general fluid flows, expanding Bose-Einstein condensates, and dynamical quantum phase transitions, the concepts of event, particle, and apparent horizons will be discussed together with the resulting quantum effects.Comment: 7 pages, 4 figure

Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity

I show that the principle of equipartition, applied to area elements of a surface which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of freedom in any diffeomorphism invariant theory of gravity. The entropy associated with these degrees of freedom matches with the Wald entropy for the theory. This result also allows one to attribute an entropy density to the spacetime in a natural manner. The field equations of the theory can then be obtained by extremising this entropy. Moreover, when the microscopic degrees of freedom are in local thermal equilibrium, the spacetime entropy of a bulk region resides on its boundary.Comment: v1: 20 pages; no figures. v2: Sec 4 added; 23 page