On 3+1 anti-de Sitter and de Sitter Lie bialgebras with dimensionful deformation parameters

We analyze among all possible quantum deformations of the 3+1 (anti)de Sitter algebras, so(3,2) and so(4,1), which have two specific non-deformed or primitive commuting operators: the time translation/energy generator and a rotation. We prove that under these conditions there are only two families of two-parametric (anti)de Sitter Lie bialgebras. All the deformation parameters appearing in the bialgebras are dimensionful ones and they may be related to the Planck length. Some properties conveyed by the corresponding quantum deformations (zero-curvature and non-relativistic limits, space isotropy,...) are studied and their dual (first-order) non-commutative spacetimes are also presented.Comment: 7 pages. Communication presented in the XIII Int.Colloq. Integrable Systems and Quantum Groups, June 17-19, 2004, Prague, Czech Republic. Some misprints and dimensions of parameters have been fitte

Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups

The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel'd-double and the Poisson-Lie structure underlying the $\kappa$-deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson-Lie algebras. As a consequence, the non-commutative (2+1)D spacetimes that generalize the $\kappa$-Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce non-commutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related with 2+1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related with the Planck length, and the existence of a kind of "duality" between the cosmological constant and the Planck scale is also envisaged.Comment: 25 pages. Updated version with more content, comments and reference

A non-commutative Minkowskian spacetime from a quantum AdS algebra

A quantum deformation of the conformal algebra of the Minkowskian spacetime in $(3+1)$ dimensions is identified with a deformation of the $(4+1)$-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known $\kappa$-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian spacetime is constructed through the full (all orders) dual quantum group spanned by deformed Poincar\'e and dilation symmetries. Although Lorentz invariance is lost, the resulting non-commutative spacetime is quantum group covariant, preserves space isotropy and, furthermore, can be interpreted as a generalization of the $\kappa$-Minkowski space in which a variable fundamental scale (Planck length) appears.Comment: Revised version accepted for pubblication on PLB. Latex file, 9 page

Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations

We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra sl(2,R). We investigate the classical Drinfel'd double of a "hybrid" deformation of sl(2,R) that depends on two parameters (\eta,z). With an appropriate choice of basis and real structure, this Drinfel'd double agrees with the 3d anti-de Sitter algebra. The deformation parameter \eta is related to the cosmological constant, while z is identified with the inverse of the speed of light and defines the signature of the metric. We generalise this result to de Sitter space, the three-sphere and 3d hyperbolic space through analytic continuation in \eta and z; we also investigate the limits of vanishing \eta and z, which yield the flat spacetimes (Minkowski and Euclidean spaces) and Newtonian models, respectively.Comment: 12 pages; minor changes, additional reference

A Standardized Index for Assessing Seawater Intrusion in Coastal Aquifers: The SITE Index

A large number of coastal aquifers worldwide are impacted by seawater intrusion. A major aim of European Directives 2000/60/EC and 2006/118/EC is to achieve good ecological status in groundwater bodies, including coastal aquifers. To this goal, information is needed about the current state of, and changes over time in, individual aquifers. This information can be obtained by applying methods that determine the status of aquifers in an uncomplicated manner. Methods for this type of assessment must comply with three essential criteria. First, calculation of the index must be straightforward and should be based on easy-to-obtain or commonly available data. Next, the index should be able to highlight important characteristics in understandable terms. Finally, the results should be objective and should be expressed in such a way that different time periods and different aquifers can be compared. In this paper we describe the development of a method to characterize seawater intrusion that meets these criteria and is based on four basic parameters: surface area, intensity, temporality, and evolution. Each parameter is determined by specific calculations derived from the groundwater chloride concentrations. Results are specified as a numerical index and an alphanumeric code. This index, known as SITE, has been applied to four Mediterranean coastal aquifers. The standardized results allowed us to discriminate between, and objectively compare the status of these groundwater bodies. Further, this index will make it possible to prioritize management actions and evaluate the effectiveness of these actions over time

Spatial characterization of the seawater upconing process in a coastal Mediterranean aquifer (Plana de Castellon, Spain): Evolution and controls

In this contribution, we describe the formation and evolution of the upconing process in a Mediterranean coastal aquifer. The study area has experienced severe salinization over the last 40 years because of intensive exploitation of groundwater. We used historical and current records of piezometric levels and chloride concentrations to trace the development of the salinization of the aquifer. We defined the 3D shape of the saline wedge from the spatial distribution of chloride concentrations and vertical well logs of electrical conductivity using monitoring network data. Upconing first appeared in the early 90s and has continued until the present day. In this study, we examined the intensity of the upconing process. Dry periods and the associated increases in pumping caused the advance of seawater intrusion. The sharp reduction in groundwater withdrawals over the last 10 years has caused the saline wedge to move backwards, although the ongoing pumping and the climate conditions mean that this retreat is quite slow

Spatial characterization of the seawater upconing process in a coastal Mediterranean aquifer (Plana de Castellón, Spain): evolution and controls

In this contribution, we describe the formation and evolution of the upconing process in a Mediterranean coastal aquifer. The study area has experienced severe salinization over the last 40 years because of intensive exploitation of groundwater. We used historical and current records of piezometric levels and chloride concentrations to trace the development of the salinization of the aquifer. We defined the 3D shape of the saline wedge from the spatial distribution of chloride concentrations and vertical well logs of electrical conductivity using monitoring network data. Upconing first appeared in the early 90s and has continued until the present day. In this study, we examined the intensity of the upconing process. Dry periods and the associated increases in pumping caused the advance of seawater intrusion. The sharp reduction in groundwater withdrawals over the last 10 years has caused the saline wedge to move backwards, although the ongoing pumping and the climate conditions mean that this retreat is quite slow

Interplay between curvature and Planck-scale effects in astrophysics and cosmology

Several recent studies have considered the implications for astrophysics and cosmology of some possible nonclassical properties of spacetime at the Planck scale. The new effects, such as a Planck-scale-modified energy-momentum (dispersion) relation, are often inferred from the analysis of some quantum versions of Minkowski spacetime, and therefore the relevant estimates depend heavily on the assumption that there could not be significant interplay between Planck-scale and curvature effects. We here scrutinize this assumption, using as guidance a quantum version of de Sitter spacetime with known Inonu-Wigner contraction to a quantum Minkowski spacetime. And we show that, contrary to common (but unsupported) beliefs, the interplay between Planck-scale and curvature effects can be significant. Within our illustrative example, in the Minkowski limit the quantum-geometry deformation parameter is indeed given by the Planck scale, while in the de Sitter picture the parameter of quantization of geometry depends both on the Planck scale and the curvature scalar. For the much-studied case of Planck-scale effects that intervene in the observation of gamma-ray bursts we can estimate the implications of "quantum spacetime curvature" within robust simplifying assumptions. For cosmology at the present stage of the development of the relevant mathematics one cannot go beyond semiheuristic reasoning, and we here propose a candidate approximate description of a quantum FRW geometry, obtained by patching together pieces (with different spacetime curvature) of our quantum de Sitter. This semiheuristic picture, in spite of its limitations, provides rather robust evidence that in the early Universe the interplay between Planck-scale and curvature effects could have been particularly significant.Comment: 26 pages

A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra

A mass-like quantum Weyl-Poincare algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, a new relativistic theory with two observer-independent scales (or DSR theory). Deformed momentum representation, finite boost transformations, range of rapidity, energy and momentum, as well as position and velocity operators are explicitly studied and compared with those of previous DSR theories based on kappa-Poincare algebra. The main novelties of the DSR theory here presented are the new features of momentum saturation and a new type of deformed position operators.Comment: 13 pages, LaTeX; some references and figures added, and terminology is more precis