Remarks on the Entropy of Non-Stationary Black Holes

The definition of entropy obtained for stationary black holes is extended in this paper to the case of non-stationary black holes. Entropy is defined as a macroscopical thermodynamical quantity which satisfies the first principle of thermodynamics. In the non-stationary case a volume term appears since the solution does not admit a Killing vector

Covariant Charges in Chern-Simons AdS_3 Gravity

We try to give hereafter an answer to some open questions about the definition of conserved quantities in Chern-Simons theory, with particular reference to Chern-Simons AdS_3 Gravity. Our attention is focused on the problem of global covariance and gauge invariance of the variation of Noether charges. A theory which satisfies the principle of covariance on each step of its construction is developed, starting from a gauge invariant Chern-Simons Lagrangian and using a recipe developed in gr-qc/0110104 and gr-qc/0107074 to calculate the variation of conserved quantities. The problem to give a mathematical well-defined expression for the infinitesimal generators of symmetries is pointed out and it is shown that the generalized Kosmann lift of spacetime vector fields leads to the expected numerical values for the conserved quantities when the solution corresponds to the BTZ black hole. The fist law of black holes mechanics for the BTZ solution is then proved and the transition between the variation of conserved quantities in Chern-Simons AdS_3 Gravity theory and the variation of conserved quantities in General Relativity is analysed in detail.Comment: 30 pages, no figures. References adde

A non-geodesic motion in the R^-1 theory of gravity tuned with observations

In the general picture of high order theories of gravity, recently, the R^-1 theory has been analyzed in two different frameworks. In this letter a third context is added, considering an explicit coupling between the R^-1 function of the Ricci scalar and the matter Lagrangian. The result is a non-geodesic motion of test particles which, in principle, could be connected with Dark Matter and Pioneer anomaly problems.Comment: Accepted for Modern Physics Letters

Dark Energy Dominance and Cosmic Acceleration in First Order Formalism

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation.Comment: 21 pages, LaTeX file, no figures. Replaced version to be published on Phys. Rev.

Gravitational Lensing and f(R) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f(R) extended theories of gravity. Starting from an exact solution of the f(R) field equations, which corresponds to the Schwarzschild-de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the non linearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.Comment: 7 Pages, RevTex, 1 eps figure; references added; revised to match the version accepted for publication in General Relativity and Gravitatio

Hoffmann-Infeld Black Hole Solutions in Lovelock Gravity

Five-dimensional black holes are studied in Lovelock gravity coupled to Hoffmann-Infeld non-linear electrodynamics. It is shown that some of these solutions present a double peak behavior of the temperature as a function of the horizon radius. This feature implies that the evaporation process, though drastic for a period, leads to an eternal black hole remnant. Moreover, the form of the caloric curve corresponds to the existence of a plateau in the evaporation rate, which implies that black holes of intermediate scales turn out to be unstable. The geometrical aspects, such as the absence of conical singularity, the structure of horizons, etc. are also discussed. In particular, solutions that are asymptotically AdS arise for special choices of the parameters, corresponding to charged solutions of five-dimensional Chern-Simons gravity.Comment: 6 pages, 5 figures, Revtex4. References added and comments clarified; version accepted for publicatio

Dark Energy and Viscous Cosmology

Singularities in the dark energy universe are discussed, assuming that there is a bulk viscosity in the cosmic fluid. In particular, it is shown how the physically natural assumption of letting the bulk viscosity be proportional to the scalar expansion in a spatially flat FRW universe can drive the fluid into the phantom region (w -1) in the non-viscous case.Comment: 11 pages. Printing error in eq.(23) corrected. To appear in Gen. Rel. Gra

Classical Euclidean wormhole solutions in Palatini f(R~)f(\tilde{R}) cosmology

We study the classical Euclidean wormholes in the context of extended theories of gravity. With no loss of generality, we use the dynamical equivalence between $f(\tilde{R})$ gravity and scalar-tensor theories to construct a point-like Lagrangian in the flat FRW space time. We first show the dynamical equivalence between Palatini $f(\tilde{R})$ gravity and the Brans-Dicke theory with self-interacting potential, and then show the dynamical equivalence between the Brans-Dicke theory with self-interacting potential and the minimally coupled O'Hanlon theory. We show the existence of new Euclidean wormhole solutions for this O'Hanlon theory and, for an special case, find out the corresponding form of $f(\tilde{R})$ having wormhole solution. For small values of the Ricci scalar, this $f(\tilde{R})$ is in agreement with the wormhole solution obtained for higher order gravity theory $\tilde{R}+\epsilon \tilde{R}^2,\epsilon<0$.Comment: 11 page