Universality of Einstein Equations for the Ricci Squared Lagrangians

It has been recently shown that, in the first order (Palatini) formalism, there is universality of Einstein equations and Komar energy-momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar's expression for the energy-momentum complex. In this paper a similar analysis (also in the framework of the first order formalism) is performed for all nonlinear Lagrangians depending on the (symmetrized) Ricci square invariant. The main result is that the universality of Einstein equations and Komar energy-momentum complex also extends to this case (modulo a conformal transformation of the metric).Comment: 21 pages, Late

Transition Contour Synthesis with Dynamic Patch Transitions

In this article, we present a novel approach for modulating the shape of transitions between terrain materials to produce detailed and varied contours where blend resolution is limited. Whereas texture splatting and blend mapping add detail to transitions at the texel level, our approach addresses the broader shape of the transition by introducing intermittency and irregularity. Our results have proven that enriched detail of the blend contour can be achieved with a performance competitive to existing approaches without additional texture, geometry resources, or asset preprocessing. We achieve this by compositing blend masks on-the-fly with the subdivision of texture space into differently sized patches to produce irregular contours from minimal artistic input. Our approach is of particular importance for applications where GPU resources or artistic input is limited or impractical

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part II: BCEA Theory

The BTZ black hole solution for (2+1)-spacetime is considered as a solution of a triad-affine theory (BCEA) in which topological matter is introduced to replace the cosmological constant in the model. Conserved quantities and entropy are calculated via Noether theorem, reproducing in a geometrical and global framework earlier results found in the literature using local formalisms. Ambiguities in global definitions of conserved quantities are considered in detail. A dual and covariant Legendre transformation is performed to re-formulate BCEA theory as a purely metric (natural) theory (BCG) coupled to topological matter. No ambiguities in the definition of mass and angular momentum arise in BCG theory. Moreover, gravitational and matter contributions to conserved quantities and entropy are isolated. Finally, a comparison of BCEA and BCG theories is carried out by relying on the results obtained in both theories.Comment: PlainTEX, 20 page

Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

A general recipe to define, via Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge-Teitelboim-like approach applied to the variation of Noether conserved quantities. The Hamiltonian for General Relativity in presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.Comment: 29 pages with 1 figur

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting

The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription by Wald et al. we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.Comment: PlainTEX, 16 pages. Revised version 1.

Further Extended Theories of Gravitation: Part I

We shall here propose a class of relativistic theories of gravitation, based on a foundational paper of Ehlers Pirani and Schild (EPS).All "extended theories of gravitation" (also known as f(R) theories) in Palatini formalism are shown to belong to this class. In a forthcoming paper we shall show that this class of theories contains other more general examples. EPS framework helps in the interpretation and solution of these models that however have exotic behaviours even compared to f(R) theories.Comment: 10 pages. Some refs adde

The Universality of Einstein Equations

It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as independent variables, leads to ``universal'' equations. If the dimension $n$ of space--time is greater than two these universal equations are Einstein equations for a generic Lagrangian and are suitably replaced by other universal equations at bifurcation points. We show that bifurcations take place in particular for conformally invariant Lagrangians $L=R^{n/2} \sqrt g$ and prove that their solutions are conformally equivalent to solutions of Einstein equations. For 2--dimensional space--time we find instead that the universal equation is always the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the Levi--Civita connection of the metric and an additional vectorfield ensuing from conformal invariance. As an example, we investigate in detail some polynomial Lagrangians and discuss their bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9

Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)

We present an alternative field theoretical approach to the definition of conserved quantities, based directly on the field equations content of a Lagrangian theory (in the standard framework of the Calculus of Variations in jet bundles). The contraction of the Euler-Lagrange equations with Lie derivatives of the dynamical fields allows one to derive a variational Lagrangian for any given set of Lagrangian equations. A two steps algorithmical procedure can be thence applied to the variational Lagrangian in order to produce a general expression for the variation of all quantities which are (covariantly) conserved along the given dynamics. As a concrete example we test this new formalism on Einstein's equations: well known and widely accepted formulae for the variation of the Hamiltonian and the variation of Energy for General Relativity are recovered. We also consider the Einstein-Cartan (Sciama-Kibble) theory in tetrad formalism and as a by-product we gain some new insight on the Kosmann lift in gauge natural theories, which arises when trying to restore naturality in a gauge natural variational Lagrangian.Comment: Latex file, 31 page

Born-Infeld-Einstein theory with matter

The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for the scalar field that produces field equations identical to the usual Einstein field equations minimally coupled to a scalar field. In the electromagnetic and Dirac cases the field equations reproduce the standard equations only to lowest order. The spherically symmetric electrovac equations are studied in detail. It is shown that the resulting Einstein equations correspond to gravity coupled to a modified Born-Infeld theory. It is also shown that point charges are not allowed. All particles must have a finite size. Mass terms for the fields are also considered.Comment: 12 pages, LaTe

Participatory assessment of the Toliara Bay reef fishery, southwest Madagascar

In order to ensure the sustainable management of reef fisheries, it is necessary to obtain data about the impacts of these fisheries on both fish  resources and the ecosystems that sustain them. Ecosystem - based surveys provide such information, but are difficult to implement because of high technical, financial and human resource requirements. In this regard participatory assessment methods have the potential to increase the amount of data collected at low cost, while taking advantage of local traditional ecological knowledge. In order to investigate the reef fishery of Toliara Bay, southwest Madagascar, we used participatory fish survey and interview data collected on site. These methods included: (i) monitoring of catch landings over six months by wholesale fish merchants, (ii) household surveys of fishing catch and effort, and fish consumption conducted by school children, and (iii) semi - structured interviews of reef users. The landings of 1,586 fishing trips were sampled between September 2006 and February 2007, 326 households were surveyed by trained school children in January 2007, and 70 reef users were interviewed in July/August 2006. Data collected by participants were compiled and compared to reference values when available, allowing an assessment of the sustainability of the reef fishery. The results of this study confirm the unsustainable nature of resource exploitation and underline the need for rapid management responses in order to reverse this trend. It also highlights the great potential of participatory assessment methods for gathering large amounts of relevant information on the status and evolution of the ecosystem upon which the fishery depends, while promoting education and awareness about the conservation and sustainable use of natural resources.Bien que les pêcheries récifales ne contribuent que marginalement aux captures de pêche mondiales, elles restent une source majeure de revenus et de protéines pour des millions de personnes, en particulier dans les pays en voie de développement. Afin de s’assurer de la bonne gestion de ces pêcheries, il est nécessaire de disposer d’informations sur l’état des ressources et des écosystèmes dont elles dépendent. Mener de telles études est d’autant plus compliqué que les pêcheries en milieu corallien portent sur un large éventail de stocks et d’espèces de poissons, concernent de nombreux pêcheurs et supposent diverses méthodes de captures, et empruntent un grand nombre de canaux de distribution. De plus, ces pêcheries sont souvent considérées de moindre valeur par les gouvernements qui leur octroient donc peu de moyens humains et financiers. Face à ces problèmes, l’implication de la société civile dans les programmes de suivi, appelé suivi participatif, semble en mesure d’apporter des solutions, d’autant que les suivis participatifs présentent l’avantage d’accroître le nombre de données collectées à moindre coût, tout en profitant des connaissances écologiques empiriques qui sont disponibles localement. Afin d’évaluer la pérennité de la pêcherie récifale de la baie de Toliara dans le sud ouest de Madagascar, des méthodes de suivi participatif ont été expérimentées. Ces méthodes consistent à mettre en oeuvre : (i) des suivis des débarquements pendant six mois impliquant des mareyeuses, (ii) des enquêtes auprès des ménages, réalisées par des écoliers préalablement formés, afin de recueillir des informations sur l’effort de pêche, les captures et la consommation de poisons, (iii) des entretiens semi - directifs avec des usagers du milieu marin. Ainsi, entre 2006 et 2007, 1586 sorties de pêche ont été échantillonnées, et 326 ménages et 70 usagers ont fait l’objet d’enquêtes. Les données collectées par les membres de la communauté locale ont été analysées afin d’évaluer la pérennité de la pêcherie dans la baie de Toliara. Les résultats de l’étude confirment une exploitation non pérenne et soulignent la nécessité de mettre en place des mesures de gestion afin d’inverser la tendance de détérioration des écosystèmes de la baie. Il ressort également de cette étude que l’implication de la société civile s’avère être pertinente pour recueillir des informations sur les pêcheries récifales à faible coût. En effet, de part le nombre, la qualité, la variété et la pertinence des informations produites, les suivis participatifs contribuent utilement à l’évaluation des pêcheries récifales. Cette expérience met également en évidence le fort potentiel des suivis participatifs à contribuer au renforcement des connaissances et des capacités des communautés locales dans le domaine de la gestion des ressources marines. Ainsi, face au difficile contexte socio - économique et politique qui prévaut actuellement à Madagascar, cette approche s’avère particulièrement prometteuse pour améliorer la gestion des pêcheries traditionnelles grâce à la production d’informations sur ces pêcheries et une plus grande implication des communautés locales dans le processus de gestion.Correction to: Madagascar Conservation & Development (2011) 6, 2: 60–67. http://dx.doi.org/10.4314/mcd.v6i2.4; published online 22 December 2011On p. 63, ‘mt/y’ should be metric ton per year and not million ton per year.Sentence should read “With the results of the household survey we were able to estimate a total production for the Toliara Bay fishery at 2,700 ± 436 metric tons per year (mt/y), and the annual yield at 14.2±2.3mt/y/km2.&#8221