Catching homologies by geometric entropy

A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale--free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.Comment: 12 pages, 2 Figure

Relativistic Charged Spheres II: Regularity and Stability

We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by exact solutions of Einstein's field equations. A family of these solutions had already be found (de Felice et al., 1995) but here we generalize that result to cases with different charge distribution within the spheres and show, in an appropriate parameter space, that the set of such physically reasonable solutions has a non zero measure. We also perform a perturbation analysis and identify the solutions which are stable against adiabatic radial perturbations. We then suggest that the stable configurations can be considered as classic models of charged particles. Finally our results are used to show that a conjecture of Kristiansson et al. (1998) is incorrect.Comment: revtex, 13 pages. five EPS figures. Accepted by CQ

Strains and Jets in Black Hole Fields

We study the behaviour of an initially spherical bunch of particles emitted along trajectories parallel to the symmetry axis of a Kerr black hole. We show that, under suitable conditions, curvature and inertial strains compete to generate jet-like structures.Comment: To appear in the Proceedings of the Spanish Relativity Meeting 2007 held in Tenerife (Spain) 3 Figure

Tracing a relativistic Milky Way within the RAMOD measurement protocol

Advancement in astronomical observations and technical instrumentation implies taking into account the general relativistic effects due the gravitational fields encountered by the light while propagating from the star to the observer. Therefore, data exploitation for Gaia-like space astrometric mission (ESA, launch 2013) requires a fully relativistic interpretation of the inverse ray-tracing problem, namely the development of a highly accurate astrometric models in accordance with the geometrical environment affecting light propagation itself and the precepts of the theory of measurement. This could open a new rendition of the stellar distances and proper motions, or even an alternative detection perspective of many subtle relativistic effects suffered by light while it is propagating and subsequently recorded in the physical measurements.Comment: Proceeding for "Relativity and Gravitation, 100 Years after Einstein in Prague" to be published by Edition Open Access, revised versio

Information geometric complexity of a trivariate Gaussian statistical model

We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult is making macroscopic predictions about a systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint, seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.Comment: 16 pages, 1 figur

Information geometric methods for complexity

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.Comment: review article, 60 pages, no figure

Asymptotic latent solitons, black strings and black branes in f(R)-gravity

We investigate nonlinear f(R) theories in the Kaluza-Klein models with toroidal compactification of extra dimensions. A point-like matter source has the dust-like equation of state in our three dimensions and nonzero equations of state in the extra dimensions. We obtain solutions of linearized Einstein equations with this matter source taking into account effects of nonlinearity of the model. There are two asymptotic regions where solutions satisfy the gravitational tests at the same level of accuracy as General Relativity. According to these asymptotic regions, there are two classes of solutions. We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known result of the linear theory. The asymptotic black strings and black branes are particular cases of these asymptotic solutions. The second class of asymptotic solitons exists only in multidimensional nonlinear models. The main feature for both of these classes of solutions is that the matter sources have tension in the extra dimensions.Comment: RevTex4 5 pages, no figure

The Formation of non-Keplerian Rings of Matter about Compact Stars

The formation of energetic rings of matter in a Kerr spacetime with an outward pointing acceleration field does not appear to have previously been noted as a relativistic effect. In this paper we show that such rings are a gravimagneto effect with no Newtonian analog, and that they do not occur in the static limit. The energy efficiency of these rings can, depending of the strength of the acceleration field, be much greater than that of Keplerian disks. The rings rotate in a direction opposite to that of compact star about which they form. The size and energy efficiency of the rings depend on the fundamental parameters of the spacetime as well as the strength the acceleration field.Comment: 19 pages, 7 figures, 1 diagram. Figures are included in the text using the "graphicx" package. If you do not have this package you can use epsfig, or another package as long as you alter the tex file appropriately. Alternatively you could print the figures out seperatel

Weak-field limit of f(R)-gravity in three and more spatial dimensions

We investigate a point-like massive source in non-linear f(R) theories in the case of arbitrary number of spatial dimensions D\geq 3. If D>3 then extra dimensions undergo toroidal compactification. We consider a weak-field approximation with Minkowski and de Sitter background solutions. In both these cases point-like massive sources demonstrate good agreement with experimental data only in the case of ordinary three-dimensional (D=3) space. We generalize this result to the case of perfect fluid with dust-like equations of state in the external and internal spaces. This perfect fluid is uniformly smeared over all extra dimensions and enclosed in a three-dimensional sphere. In ordinary three dimensional (D=3) space, our formulas are useful for experimental constraints on parameters of f(R) models.Comment: 8 pages, Revtex4, no figure

Cosmological dynamics of fourth order gravity with a Gauss-Bonnet term

We consider cosmological dynamics in fourth order gravity with both $f(R)$ and $\Phi(\mathcal {G})$ correction to the Einstein gravity ($\mathcal{G}$ is the Gauss-Bonnet term). The particular case for which both terms are equally important on power-law solutions is described. These solutions and their stability are studied using the dynamical system approach. We also discuss condition of existence and stability of de Sitter solution in a more general situation of power-law $f$ and $\Phi$.Comment: published version, references update