Entanglement entropy, black holes and holography

We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure states with this property have long-range correlations between interior and exterior modes and are constructed by purification of the desired density matrix. We show that imposing a no-gravitational collapse condition on the pure state is sufficient to exclude faster than area law entropy scaling. This observation leads to an interpretation of holography as an upper bound on the realizable entropy (entanglement or von Neumann) of a region, rather than on the dimension of its Hilbert space.Comment: 4 pages, revte

Four decades of water recycling in Atlantis (Western Cape, South Africa): Past, present and future

The primary aquifer at Atlantis (Western Cape, South Africa) is ideally suited for water supply and the indirect recycling of urban stormwater runoff and treated domestic wastewater for potable purposes. The relatively thin, sloping aquifer requires careful management of the artificial recharge and abstraction for balancing water levels. Water quality management is a further key issue at Atlantis for ensuring the highest quality potable water. Groundwater quality varies from point to point in the aquifer, while urban runoff and wastewater qualities vary greatly. The layout of the town allows for the separation of stormwater from the residential and industrial areas as well as separate treatment of domestic and industrial wastewater. This permits safe artificial recharge of the various water quality portions at different points in the aquifer, either for recycling or for preventing seawater intrusion. All of the management actions are dependent on detailed data collection and this paper describes the various parts of the system, describes the data collection activities, and provides results of the monitoring and aquifer responses over the past four decades. Challenges related to iron fouling of production boreholes are also described. The presence of emerging contaminants was studied in 2008 but requires follow-up research for establishing the extent of any possible threat to water recycling. In order to address the shortcomings of the system a risk management plan based on the Hazard Analysis and Critical Control Points approach was developed. Lessons learnt from the Atlantis experience can be transferred to other potential sites for establishment of similar systems in arid and semi-arid areas of South Africa and the African continent.Keywords: Atlantis, managed aquifer recharge, water recycling, groundwater, stormwater, wastewater, monitorin

On Traversable Lorentzian Wormholes in the Vacuum Low Energy Effective String Theory in Einstein and Jordan Frames

Three new classes (II-IV) of solutions of the vacuum low energy effective string theory in four dimensions are derived. Wormhole solutions are investigated in those solutions including the class I case both in the Einstein and in the Jordan (string) frame. It turns out that, of the eight classes of solutions investigated (four in the Einstein frame and four in the corresponding string frame), massive Lorentzian traversable wormholes exist in five classes. Nontrivial massless limit exists only in class I Einstein frame solution while none at all exists in the string frame. An investigation of test scalar charge motion in the class I solution in the two frames is carried out by using the Plebanski-Sawicki theorem. A curious consequence is that the motion around the extremal zero (Keplerian) mass configuration leads, as a result of scalar-scalar interaction, to a new hypothetical "mass" that confines test scalar charges in bound orbits, but does not interact with neutral test particles.Comment: 18 page

Synergistic warm inflation

We consider an alternative warm inflationary scenario in which $n$ scalar fields coupled to a dissipative matter fluid cooperate to produce power--law inflation. The scalar fields are driven by an exponential potential and the bulk dissipative pressure coefficient is linear in the expansion rate. We find that the entropy of the fluid attains its asymptotic value in a characteristic time proportional to the square of the number of fields. This scenario remains nearly isothermal along the inflationary stage. The perturbations in energy density and entropy are studied in the long--wavelength regime and seen to grow roughly as the square of the scale factor. They are shown to be compatible with COBE measurements of the fluctuations in temperature of the CMB.Comment: 13 pages, Revtex 3 To be published in Physical Review

Adiabatic perturbations in pre big bang models: matching conditions and scale invariance

At low energy, the four-dimensional effective action of the ekpyrotic model of the universe is equivalent to a slightly modified version of the pre big bang model. We discuss cosmological perturbations in these models. In particular we address the issue of matching the perturbations from a collapsing to an expanding phase in full generality. We show that, generically, one obtains $n=0$ for the spectrum of scalar perturbations in the original pre big model (with vanishing potential). When an exponential potential for the dilaton is included, a scale invariant spectrum ($n=1$) of adiabatic scalar perturbations is produced under very generic matching conditions, both in a modified pre big bang and ekpyrotic scenario. We also derive general results valid for power law scale factors matched to a radiation dominated era.Comment: 11 pages, 1 figure, revised version with small corrections to match version in print. Results and conclusions unchange

Hydrodynamics and Flow

In this lecture note, we present several topics on relativistic hydrodynamics and its application to relativistic heavy ion collisions. In the first part we give a brief introduction to relativistic hydrodynamics in the context of heavy ion collisions. In the second part we present the formalism and some fundamental aspects of relativistic ideal and viscous hydrodynamics. In the third part, we start with some basic checks of the fundamental observables followed by discussion of collective flow, in particular elliptic flow, which is one of the most exciting phenomenon in heavy ion collisions at relativistic energies. Next we discuss how to formulate the hydrodynamic model to describe dynamics of heavy ion collisions. Finally, we conclude the third part of the lecture note by showing some results from ideal hydrodynamic calculations and by comparing them with the experimental data.Comment: 40 pages, 35 figures; lecture given at the QGP Winter School, Jaipur, India, Feb.1-3, 2008; to appear in Springer Lecture Notes in Physic

Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories

We present cosmological perturbations of kinetic components based on relativistic Boltzmann equations in the context of generalized gravity theories. Our general theory considers an arbitrary number of scalar fields generally coupled with the gravity, an arbitrary number of mutually interacting hydrodynamic fluids, and components described by the relativistic Boltzmann equations like massive/massless collisionless particles and the photon with the accompanying polarizations. We also include direct interactions among fluids and fields. The background FLRW model includes the general spatial curvature and the cosmological constant. We consider three different types of perturbations, and all the scalar-type perturbation equations are arranged in a gauge-ready form so that one can implement easily the convenient gauge conditions depending on the situation. In the numerical calculation of the Boltzmann equations we have implemented four different gauge conditions in a gauge-ready manner where two of them are new. By comparing solutions solved separately in different gauge conditions we can naturally check the numerical accuracy.Comment: 26 pages, 9 figures, revised thoroughly, to appear in Phys. Rev.

Perturbations of brane worlds

We consider cosmological models where the universe, governed by Einstein's equations, is a piece of a five dimensional double-sided anti-de Sitter spacetime (that is, a "$Z_2$-symmetric bulk") with matter confined to its four dimensional Robertson-Walker boundary or "brane". We study the perturbations of such models. We use conformally minkowskian coordinates to disentangle the contributions of the bulk gravitons and of the motion of the brane. We find the restrictions put on the bulk gravitons when matter on the brane is taken to be a scalar field and we solve in that case the brane perturbation equations.Comment: 19 pages, no figures, RevTex, version to appear in Phys.Rev.D; minor changes in chap.V, polarisation tensor at page 13 correcte

Inflation and Braneworlds: Degeneracies and Consistencies

Scalar and tensor perturbations arising in an inflationary braneworld scenario driven by a single scalar field are considered, where the bulk on either side of the brane corresponds to Anti-de Sitter spaces with different cosmological constants. A consistency relation between the two spectra is derived and found to have an identical form to that arising in standard single-field inflation based on conventional Einstein gravity. The dS/CFT correspondence may provide further insight into the origin of this degeneracy. Possible ways of lifting such a degeneracy are discussed.Comment: 10 page