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

Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity

A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the subleading terms in the entropy in different dimensions and to behaviour in different states. It is conjectured, on the base of relation between the entropy and the action, that in a fundamental theory the ground state entanglement entropy per unit area equals $1/(4G_N)$, where $G_N$ is the Newton constant in the low-energy gravity sector of the theory. The conjecture opens a new avenue in analogue gravity models. For instance, in higher dimensional condensed matter systems, which near a critical point are described by relativistic QFT's, the entanglement entropy density defines an effective gravitational coupling. By studying the properties of this constant one can get new insights in quantum gravity phenomena, such as the universality of the low-energy physics, the renormalization group behavior of $G_N$, the statistical meaning of the Bekenstein-Hawking entropy.Comment: 13 pages, published version, minor changes in the abstract, new reference

Deformed Special Relativity as an effective theory of measurements on quantum gravitational backgrounds

In this article we elaborate on a recently proposed interpretation of DSR as an effective measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations. We provide several heuristic arguments to explain how such a new theory can emerge and discuss the possible observational consequences of this framework.Comment: 11 pages, no figure

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

Panel Discussion: Regulation of Foreign Investment and Trade

Article is part of the symposium: Canada and the United States: A Changing Relationship in a Changing World. Discussion among panelists regarding the new Foreign Investment and Trade Act of Canada, its implications regarding investment to Canada from the United States, tax treatment, and other investment issues

Fundamental limitations on "warp drive" spacetimes

"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. We verify the non-perturbative violation of the classical energy conditions of the Alcubierre and Natario warp drive spacetimes and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the non-relativistic warp-bubble velocity. We are primarily interested in a secondary feature of the warp drive that has not previously been remarked upon, if it could be built, the warp drive would be an example of a "reaction-less drive". For both the Alcubierre and Natario warp drives we find that the occurrence of significant energy condition violations is not just a high-speed effect, but that the violations persist even at arbitrarily low speeds. An interesting feature of this construction is that it is now meaningful to place a finite mass spaceship at the center of the warp bubble, and compare the warp field energy with the mass-energy of the spaceship. There is no hope of doing this in Alcubierre's original version of the warp-field, since by definition the point in the center of the warp bubble moves on a geodesic and is "massless". That is, in Alcubierre's original formalism and in the Natario formalism the spaceship is always treated as a test particle, while in the linearized theory we can treat the spaceship as a finite mass object. For both the Alcubierre and Natario warp drives we find that even at low speeds the net (negative) energy stored in the warp fields must be a significant fraction of the mass of the spaceship.Comment: 18 pages, Revtex4. V2: one reference added, some clarifying comments and discussion, no physics changes, accepted for publication in Classical and Quantum Gravit

Can dark matter be a Bose-Einstein condensate?

We consider the possibility that the dark matter, which is required to explain the dynamics of the neutral hydrogen clouds at large distances from the galactic center, could be in the form of a Bose-Einstein condensate. To study the condensate we use the non-relativistic Gross-Pitaevskii equation. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. Hence dark matter can be described as a non-relativistic, Newtonian Bose-Einstein gravitational condensate gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index $n=1$. To test the validity of the model we fit the Newtonian tangential velocity equation of the model with a sample of rotation curves of low surface brightness and dwarf galaxies, respectively. We find a very good agreement between the theoretical rotation curves and the observational data for the low surface brightness galaxies. The deflection of photons passing through the dark matter halos is also analyzed, and the bending angle of light is computed. The bending angle obtained for the Bose-Einstein condensate is larger than that predicted by standard general relativistic and dark matter models. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the Bose-Einstein condensate dark matter model and other dark matter models.Comment: 20 pages, 7 figures, accepted for publication in JCAP, references adde

Microlensing by natural wormholes: theory and simulations

We provide an in depth study of the theoretical peculiarities that arise in effective negative mass lensing, both for the case of a point mass lens and source, and for extended source situations. We describe novel observational signatures arising in the case of a source lensed by a negative mass. We show that a negative mass lens produces total or partial eclipse of the source in the umbra region and also show that the usual Shapiro time delay is replaced with an equivalent time gain. We describe these features both theoretically, as well as through numerical simulations. We provide negative mass microlensing simulations for various intensity profiles and discuss the differences between them. The light curves for microlensing events are presented and contrasted with those due to lensing produced by normal matter. Presence or absence of these features in the observed microlensing events can shed light on the existence of natural wormholes in the Universe.Comment: 16 pages, 24 postscript figures (3 coloured), revtex style, submitted to Phys. Rev.