Universal field equations for metric-affine theories of gravity

We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field $W_\mu$ and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.Comment: 13 pages. This is a copy of the published paper. We are posting it here because of the increasing interest in f(R) theories of gravit

The Application of the Newman-Janis Algorithm in Obtaining Interior Solutions of the Kerr Metric

In this paper we present a class of metrics to be considered as new possible sources for the Kerr metric. These new solutions are generated by applying the Newman-Janis algorithm (NJA) to any static spherically symmetric (SSS) ``seed'' metric. The continuity conditions for joining any two of these new metrics is presented. A specific analysis of the joining of interior solutions to the Kerr exterior is made. The boundary conditions used are those first developed by Dormois and Israel. We find that the NJA can be used to generate new physically allowable interior solutions. These new solutions can be matched smoothly to the Kerr metric. We present a general method for finding such solutions with oblate spheroidal boundary surfaces. Finally a trial solution is found and presented.Comment: 11 pages, Latex, 4 postscript figures. To be published in Classical and Quantum Gravity. Title and abstract are now on the same pag

Singular shell embedded into a cosmological model

We generalize Israel's formalism to cover singular shells embedded in a non-vacuum Universe. That is, we deduce the relativistic equation of motion for a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker spacetime. Also, we review the embedding of a Schwarzschild mass into a cosmological model using "curvature" coordinates and give solutions with (Sch/FLRW) and without the embedded mass (FLRW).Comment: 25 pages, 2 figure

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

Effective supergravity descriptions of superstring cosmology

This text is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for `uplifting terms', i.e. methods to produce de Sitter vacua. We concentrate on N=1 and N=2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed in short at the end.Comment: 12 pages, contribution to the proceedings of the 2nd international conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelona, July 11-15, 2006, Journal of Physics

Nonextensivity and multifractality in low-dimensional dissipative systems

Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently introduced by one of us (C.T.) and characterized by the entropic index $q$. We show that general scaling arguments imply that $1/(1-q) = 1/\alpha_{min}-1/\alpha_{max}$, where $\alpha_{min}$ and $\alpha_{max}$ are the extremes of the multifractal singularity spectrum $f(\alpha)$ of the attractor. This relation is numerically checked to hold in standard one-dimensional dissipative maps. The above result sheds light on a long-standing puzzle concerning the relation between the entropic index $q$ and the underlying microscopic dynamics.Comment: 12 pages, TeX, 4 ps figure

Nonextensive Thermostatistics and the H-Theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the ``molecular chaos hypothesis". For $q>0$, the $q$-transport equation satisfies an $H$-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo

Perturbation and Variational Methods in Nonextensive Tsallis Statistics

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very natural way following the Feynman proof for the usual statistical mechanics. The inequality turns out to be form-invariant with respect to the entropic index $q$. The method is illustrated with a simple example in classical mechanics. The formalisms developed here are expected to be useful in the discussion of nonextensive systems.Comment: revte

Power-Law Sensitivity to Initial Conditions within a Logistic-like Family of Maps: Fractality and Nonextensivity

Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like maps $x_{t+1} = 1 - a | x_t |^z, (z > 1; 0 < a \le 2; t=0,1,2,...)$ The main ingredient of our approach is the generalized deviation law \lim_{\Delta x(0) -> 0} \Delta x(t) / \Delta x(0)} = [1+(1-q)\lambda_q t]^{1/(1-q)} (equal to $e^{\lambda_1 t}$ for q=1, and proportional, for large t, to $t^{1/(1-q)}$ for $q \ne 1; q \in R$ is the entropic index appearing in the recently introduced nonextensive generalized statistics). The relation between the parameter q and the fractal dimension d_f of the onset-to-chaos attractor is revealed: q appears to monotonically decrease from 1 (Boltzmann-Gibbs, extensive, limit) to -infinity when d_f varies from 1 (nonfractal, ergodic-like, limit) to zero.Comment: LaTeX, 6 pages , 5 figure

Average Entropy of a Subsystem from its Average Tsallis Entropy

In the nonextensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space dimension is $mn$, is considered, the average Tsallis entropy of an $m$-dimensional subsystem is obtained. This demonstration is expected to be useful to study systems where the usual entropy does not give satisfactory results.Comment: Revtex, 6 pages, 2 figures. To appear in Phys. Rev.