Charged rotating noncommutative black holes

In this paper we complete the program of the noncomutative geometry inspired black holes, providing the richest possible solution, endowed with mass, charge and angular momentum. After providing a prescription for employing the Newman-Janis algorithm in the case of nonvanishing stress tensors, we find regular axisymmetric charged black holes in the presence of a minimal length. We study also the new thermodynamics and we determine the corresponding higher-dimensional solutions. As a conclusion we make some consideration about possible applications.Comment: 13 pages, 3 figures, correction of a typesetting inattention, updated reference list, version accepted for publication on Physical Review

Spectral dimension of a quantum universe

In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal length by averaging the graininess of the quantum manifold in the flat space case. As a result we obtain that, for large diffusion times, the quantum spacetime behaves like a smooth differential manifold of discrete dimension. On the other hand, for smaller diffusion times, the spacetime looks like a fractal surface with a reduced effective dimension. For the specific case in which the diffusion time has the size of the minimal length, the spacetime turns out to have a spectral dimension equal to 2, suggesting a possible renormalizable character of gravity in this regime. For smaller diffusion times, the spectral dimension approaches zero, making any physical interpretation less reliable in this extreme regime. We extend our result to the presence of a background field and curvature. We show that in this case the spectral dimension has a more complicated relation with the diffusion time, and conclusions about the renormalizable character of gravity become less straightforward with respect to what we found with the flat space analysis.Comment: 5 pages, 1 figure, references added, typos corrected, title changed, final version published in Physical Review

Trace Anomaly in Quantum Spacetime Manifold

In this paper we investigate the trace anomaly in a spacetime where single events are de-localized as a consequence of short distance quantum coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does not suffer from short distance divergences. Calculation of the trace anomaly is performed using an IR regulator in order to circumvent the absence of UV infinities. The explicit form of the trace anomaly is presented and the corresponding 2D Polyakov effective action and energy momentumtensor are obtained. The vacuum expectation value of the energy momentum tensor in the Boulware, Hartle-Hawking and Unruh vacua is explicitly calculated in a (rt)-section of a recently found, noncommutative geometry inspired, Schwarzschild-like solution of the Einstein equations. The standard short distance divergences in the vacuum expectation values are regularized in agreement with the absence of UV infinities removed by quantum coordinate fluctuations.Comment: 15pages, RevTex, no figures, 1 Tabl

Aspects of noncommutative (1+1)-dimensional black holes

We present a comprehensive analysis of the spacetime structure and thermodynamics of $(1+1)-$dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length $\sqrt{\theta}$ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass $M$, cosmological constant $\Lambda$, etc...), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.Comment: 24 pages, 12 figures, some comments added, conclusions not modified, version matching that published on PR

Relativistic kinetic theory of magnetoplasmas

Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems. Such phenomena require their description in the framework of a consistent relativistic kinetic theory, rather than on relativistic MHD equations, subject to specific closure conditions. The purpose of this work is to apply the relativistic single-particle guiding-center theory developed by Beklemishev and Tessarotto, including the nonlinear treatment of small-wavelength EM perturbations which may naturally arise in such systems. As a result, a closed set of relativistic gyrokinetic equations, consisting of the collisionless relativistic kinetic equation, expressed in hybrid gyrokinetic variables, and the averaged Maxwell's equations, is derived for an arbitrary four-dimensional coordinate system.Comment: 6 pages, 1 figure. Contributed to the Proceedings of the 24th International Symposium on Rarefied Gas Dynamics, July 10-16, 2004 Porto Giardino Monopoli (Bari), Ital

Recurrent hyperinflations and learning

This paper uses a model of boundedly rational learning to account for the observations of recurrent hyperinflations in the last decade. We study a standard monetary model where the fully rational expectations assumption is replaced by a formal definition of quasi-rational learning. The model under learning is able to match remarkably well some crucial stylized facts observed during the recurrent hyperinflations experienced by several countries in the 80's. We argue that, despite being a small departure from rational expectations, quasi-rational learning does not preclude falsifiability of the model and it does not violate reasonable rationality requirements.Hyperinflations, convertibility, stabilization plans, quasi-rationality

IKT approach for quantum hydrodynamic equations

A striking feature of standard quantum mechanics is its analogy with classical fluid dynamics. In particular it is well known the Schr\"{o}dinger equation can be viewed as describing a classical compressible and non-viscous fluid, described by two (quantum) fluid fields {\rho ,% \mathbf{V}} , to be identified with the quantum probability density and velocity field. This feature has suggested the construction of a phase-space hidden-variable description based on a suitable inverse kinetic theory (IKT; Tessarotto et al., 2007). The discovery of this approach has potentially important consequences since it permits to identify the classical dynamical system which advances in time the quantum fluid fields. This type of approach, however requires the identification of additional fluid fields. These can be generally identified with suitable directional fluid temperatures $T_{QM,i}$ (for $i=1,2,3$), to be related to the expectation values of momentum fluctuations appearing in the Heisenberg inequalities. Nevertheless the definition given previously for them (Tessarotto et al., 2007) is non-unique. In this paper we intend to propose a criterion, based on the validity of a constant H-theorem, which provides an unique definition for the quantum temperatures.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

TRAINING TEACHERS TO OBSERVATION: AN APPROACH THROUGH MULTIPLE INTELLIGENCES THEORY

Observation is a daily practice in scholastic and educational contexts, but it needs to develop into a professional competence in order to be helpful. In fact, to design an educative and didactic plan and to provide useful tools, activities and tasks to their students, teachers and educators need to collect information about learners. For these reasons we’ll built a Web-Observation (Web-Ob) application, a tool able to support good practices in observation. In particular, the Web-Ob can provide Multiple Intelligences Theory as a framework through which children’s behaviors and attitudes can be observed, assessed and evaluated