Nonlinear Gravitational Lagrangians revisited

The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.Comment: Variational principles and conservation laws in General Relativity - Workshop in memory of Prof. Mauro Francaviglia - Torino, June 25th-26th, 201

Are there metric theories of gravity other than General Relativity?

Current generalizations of the classical Einstein-Hilbert Lagrangian formulation of General Relativity are reviewed. Some alternative variational principles are known to reproduce Einstein's gravitational equations, and should therefore be regarded as equivalent descriptions of the same physical model, while other variational principles ("Scalar-tensor theories" and "Higher-derivative theories") are commonly presented as truly alternative physical theories. Such theories, however, are also known to admit a reformulation which is formally identical to General Relativity (with auxiliary fields). The physical significance of this change of variables has been questioned by several authors in recent years. Here, we investigate to which extent purely affine, metric-affine, scalar-tensor and purely metric theories can be regarded as physically equivalent to GR; we show that in general this depends on which metric tensorfield is assumed to represent the true physical space-time geometry. For purely metric theories where the Lagrangian is a nonlinear function f(R) of the curvature scalar, we present an argument based on the definition of the physical energy, which leads one to regard the rescaled metric (Einstein frame) as the true physical one. As a direct consequence, the physical content of such "alternative" models is reset to coincide with General Relativity, and the "Nonlinear Gravity Theories" become nothing but exotic reformulations of General Relativity in terms of unphysical variables.Comment: 19 pages, plain TeX, no figures. Talk given at the XI Italian Conference on General Relativity and Gravitation (Trieste, Sept 26-30, 1994). improper line break (causing TeX error on line 340) fixe

A new species of Alaocyba PERRIS, 1869 (Insecta : Coleoptera : Curculionidae : Raymondionyminae) from the Maltese Islands

A new species of Alaocyba PERRIS, 1869 is described from the Maltese Islands (Central Mediterranean). Alaocyba melitensis sp.n. is the first record of this tyrrhenian genus for Malta. Ecological notes are provided.peer-reviewe

Gauge fixing in higher derivative field theories

Higher Derivative (HD) Field Theories can be transformed into second order equivalent theories with a direct particle interpretation. In a simple model involving abelian gauge symmetries we examine the fate of the possible gauge fixings throughout this process. This example is a useful test bed for HD theories of gravity and provides a nice intuitive interpretation of the "third ghost" occurring there and in HD gauge theories when a HD gauge fixing is adopted.Comment: 16 pages, Latex,( Preprint imaff 93/10

Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity

For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated to be equal to the Bekenstein-Hawking entropy. In this paper, the statistical entropy of the BTZ black hole in the higher curvature gravity is calculated and shown to be equal to the one derived by using the Noether charge method. This suggests that the equivalence of the geometrical and statistical entropies of the black hole is retained in the general diffeomorphism invariant theories of gravity. A relation between the cosmic censorship conjecture and the unitarity of the conformal field theory on the boundary of AdS is also discussed.Comment: 9 pages, no figure, submitted to Physics Letters

Tri-hamiltonian vector fields, spectral curves and separation coordinates

We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to its symplectic leaves. The frameworks is applied to Lax equations with spectral parameter, for which not only it unifies the separation techniques of Sklyanin and of Magri, but also provides a more efficient ``inverse'' procedure not involving the extraction of roots.Comment: 49 pages Section on reduction revisite

Nonlinear massive spin-two field generated by higher derivative gravity

We present a systematic exposition of the Lagrangian field theory for the massive spin-two field generated in higher-derivative gravity. It has been noticed by various authors that this nonlinear field overcomes the well known inconsistency of the theory for a linear massive spin-two field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called "(Helmholtz-)Jordan frame" and "Einstein frame". In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-two field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame. The full equations of motion and the energy-momentum tensor for the spin--two field in Einstein frame are given, and a simple but nontrivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-two field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-two field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected

Listado de tópicos en Cicerón desde la Antigüedad hasta la Alta Edad Media

Beginning with the Ciceronian divisions of rhetorical and dialectical topics as found, respectively, in the De inventione (84 BC), the De oratore (55 BC), the Partitiones oratoriae (54 BC) and the Topica (44 BC), the purpose of this study is to collect all the lists that have been transmitted from Antiquity to the early Middle Ages in order to observe, mainly through the help of several diagrams put in the appendix, their alteration, as well as their preservation.A partir de las divisiones ciceronianas de los tópicos retóricos y dialécticos, que se encuentran, respectivamente, en el De inventione (84 BC), en el De oratore (55 BC), en las Partitiones Oratoriae (54 BC) y en los Topica (44 BC), el propósito de este estudio consiste en recoger todas las listas que han sido transmitidas desde la antigüedad hasta la Alta Edad Media con el fin de observar, con la ayuda de los distintos diagramas dispuestos en el Apéndice, tanto su alteración, como su conservación