M. Francaviglia

Publications (99)38.55 Total impact

• Article: Mathematical Equivalence vs. Physical Equivalence between Extended Theories of Gravitations

  L. Fatibene, M. Francaviglia
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  ABSTRACT: We shall show that although Palatini f(R)-theories are equivalent to Brans-Dicke theories, still the first pass the Mercury precession of perihelia test, while the second do not. We argue that the two models are not physically equivalent due to a different assumptions about free fall. We shall also go through perihelia test without fixing a conformal gauge (clocks or rulers) in order to highlight what can be measured in a conformal invariant way and what cannot. We shall argue that the conformal gauge is broken by choosing a definition of clock, rulers or, equivalently, of masses.
  02/2013;
• Article: Do Barbero-Immirzi connections exist in different dimensions and signatures?

  L. Fatibene, M. Francaviglia, S. Garruto
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  ABSTRACT: We shall show that no reductive splitting of the spin group exists in dimension 3 \leq m \leq 20 other than in dimension m = 4. In dimension 4 there are reductive splittings in any signature. Euclidean and Lorentzian signatures are reviewed in particular and signature (2, 2) is investigated explicitly in detail. Reductive splittings allow to define a global SU(2)-connection over spacetime which encodes in an weird way the holonomy of the standard spin connection. The standard Barbero-Immirzi (BI) connection used in LQG is then obtained by restriction to a spacelike slice. This mechanism provides a good control on globality and covariance of BI connection showing that in dimension other than 4 one needs to provide some other mechanism to define the analogous of BI connection and control its globality.
  06/2012;
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  Available from: Mariafelicia De Laurentis

  Article: The physical foundations for the geometric structure of relativistictheories of gravitation. From General Relativity to Extended Theories ofGravity through Ehlers-Pirani-Schild approach

  S. Capozziello, M. De Laurentis, L. Fatibene, M. Francaviglia
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  ABSTRACT: We discuss in a critical way the physical foundations of geometric structure of relativistic theories of gravity by the so-called Ehlers-Pirani-Schild formalism. This approach provides a natural interpretation of the observables showing how relate them to General Relativity and to a large class of Extended Theories of Gravity. In particular we show that, in such a formalism, geodesic and causal structures of space-time can be safely disentangled allowing a correct analysis in view of observations and experiment. As specific case, we take into account the case of f(R) gravity.
  International Journal of Geometric Methods in Modern Physics 02/2012; · 0.86 Impact Factor
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  Available from: ArXiv

  Article: Fluids in Weyl Geometries

  L. Fatibene, M. Francaviglia
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  ABSTRACT: We shall investigate the consequences of non-trivial Weyl geometries on conservation laws of a fluid. In particular we shall obtain a set of properties which allow to obtain in this generalized setting the standard relation between conservation of the energy-momentum tensor and number of particles.
  09/2011;
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  Available from: silvio mercadante

  Article: About Boundary Terms in Higher Order Theories

  L. Fatibene, M. Francaviglia, S. Mercadante
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  ABSTRACT: It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particularl by the need of clarifying the issue for the purpose of applications to relativistic gravitational theories, where a bit of confusion still exists. On the contrary, as it is well known for variational principles of order k, if one fixes variables together with their derivatives (up to order k-1) on the boundary then boundary terms leave solution space invariant.
  06/2011;
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  Available from: ArXiv

  Article: On a Characterization of Geodesic Trajectories and Gravitational Motions

  L. Fatibene, M. Francaviglia, G. Magnano
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  ABSTRACT: We shall here discuss a characterization of geodesics trajectories. We shall show that the action of the gravitational field on mass particles can be essentially identified with the force that cannot be absolutely eliminated. This leads to an alternative formulation of equivalence principle.
  06/2011;
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  Available from: ArXiv

  Article: Weyl Geometries and Timelike Geodesics

  L. Fatibene, M. Francaviglia
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  ABSTRACT: In view of Ehlers-Pirani-Schild formalism, since 1972 Weyl geometries should be considered to be the most appropriate and complete framework to represent (relativistic) gravitational fields. We shall here show that in any given Lorentzian spacetime (M,g) that admits global timelike vector fields any such vector field u determines an essentially unique Weyl geometry ([g], \Gamma) such that u is \Gamma-geodesic (i.e. parallel with respect to \Gamma).
  06/2011;
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  Available from: Marco Ferraris

  Article: Inducing Barbero-Immirzi Connections along SU(2)-reductions of Bundles on Spacetime

  L. Fatibene, M. Ferraris, M. Francaviglia
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  ABSTRACT: We shall present here a general apt technique to induce connections along bundle reductions which is different from the standard restriction. This clarifies and generalizes the standard procedure to define Barbero-Immirzi (BI) connection, though on spacetime. The standard spacial BI connection used in LQG is then obtained by its spacetime version by standard restriction. The general prescription to define such a reduced connection is interesting from a mathematical viewpoint and it allows a general and direct control on transformation laws of the induced object. Moreover, unlike what happens by using standard restriction, we shall show that once a bundle reduction is given, then any connection induces a reduced connection with no constraint on the original holonomy as it happens when connections are simply restricted.
  11/2010;
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  Available from: Marco Ferraris

  Article: ADM Pseudotensors, Conserved Quantities and Covariant Conservation Laws in General Relativity

  L. Fatibene, M. Ferraris, M. Francaviglia, L. Lusanna
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  ABSTRACT: The ADM formalism is reviewed and techniques for decomposing generic components of metric, connection and curvature are obtained. These techniques will turn out to be enough to decompose not only Einstein equations but also covariant conservation laws. Then a number of independent sets of hypotheses that are sufficient (though non-necessary) to obtain standard ADM quantities (and Hamiltonian) from covariant conservation laws are considered. This determines explicitely the range in which standard techniques are equivalent to covariant conserved quantities. The Schwarzschild metric in different coordinates is then considered, showing how the standard ADM quantities fail dramatically in non-Cartesian coordinates or even worse when asymptotically flatness is not manifest; while, in view of their covariance, covariant conservation laws give the correct result in all cases. Comment: 40 pages
  07/2010;
• Article: First order Extended Gravity and the Dark side of the Universe: matching with observations

  S. Capozziello, M. De Laurentis, M. Francaviglia, S. Mercadante
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  ABSTRACT: The so called f(R)‐gravity could be, in principle, able to explain the accelerated expansion of the Universe without adding unknown forms of dark energy∕dark matter but, more simply, extending the General Relativity by generic functions of the Ricci scalar. However, a part several phenomenological models, there is no final f(R)‐theory capable of fitting all the observations and addressing all the issues related to the presence of dark energy and dark matter. Astrophysical observations are pointing out huge amounts of “dark matter” and “dark energy” needed to explain the observed large scale structures and cosmic accelerating expansion. Up to now, no experimental evidence has been found, at fundamental level, to explain such mysterious components. The problem could be completely reversed considering dark matter and dark energy as “shortcomings” of General Relativity and considering the concept of Dark Metric introduced in the companion paper of these Proceedings by the same authors.
  AIP Conference Proceedings. 06/2010; 1241(1):749-758.
• Source

  Available from: Marco Ferraris

  Article: Extended Loop Quantum Gravity

  L. Fatibene, M. Ferraris, M. Francaviglia
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  ABSTRACT: We discuss constraint structure of extended theories of gravitation (also known as f(R) theories) in the vacuum selfdual formulation introduced in ref. [1]. Comment: 7 pages, few typos corrected
  03/2010;
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  Available from: Marco Ferraris

  Article: New Cases of Universality Theorem for Gravitational Theories

  L. Fatibene, M. Ferraris, M. Francaviglia
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  ABSTRACT: The "Universality Theorem" for gravity shows that f(R) theories (in their metric-affine formulation) in vacuum are dynamically equivalent to vacuum Einstein equations with suitable cosmological constants. This holds true for a generic (i.e. except sporadic degenerate cases) analytic function f(R) and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f(R)=R). The theorem is here extended introducing in dimension 4 a 1-parameter family of invariants R' inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also selfdual formulation). It will be proven that f(R') theories so defined are dynamically equivalent to the corresponding metric-affine f(R) theory. In particular for the function f(R)=R the standard equivalence between GR and Holst Lagrangian is obtained. Comment: 10 pages, few typos corrected
  03/2010;
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  Available from: silvio mercadante

  Article: Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics

  L. Fatibene, M. Francaviglia, S. Mercadante
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  ABSTRACT: We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural Theories", that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors and so on). It is discussed how the use of Poincare'-Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as "generators of Noether symmetries", energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-called ADM laws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation "`a la Palatini" and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero-Immirzi connections). Comment: 27 pages
  01/2010;
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  Available from: silvio mercadante

  Article: Matter Lagrangians Coupled with Connections

  L. Fatibene, M. Francaviglia, S. Mercadante
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  ABSTRACT: We shall here consider extended theories of gravitation in the metric-affine formalism with matter coupled directly to the connection. A sufficiently general procedure will be exhibited to solve the resulting field equation associated to the connection. As special cases one has the no-coupling case (which is standard in f(R) literature) as well as the cases already analyzed in ref.[1].
  11/2009;
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  Available from: silvio mercadante

  Article: Further Extended Theories of Gravitation: Part II

  L. Fatibene, M. Ferraris, M. Francaviglia, S. Mercadante
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  ABSTRACT: We shall present and analyze two examples of extended theories of gravitation in Palatini formalism with matter that couples to the connection. This will show that the class of Further Extended Theories of Gravitation introduced in ref. [1] does not trivially reduce to f(R) models. It will also produce an example of theory that on-shell endowes spacetime with a non-trivial Weyl geometry where the connection is not induced by the metric structure (though it is compatible with it in the sense of Ehlers-Pirani-Schild; see ref. [2]).
  11/2009;
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  Available from: Marco Ferraris

  Article: Further Extended Theories of Gravitation: Part I

  M. Di Mauro, L. Fatibene, M. Ferraris, M. Francaviglia
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  ABSTRACT: We shall here propose a class of relativistic theories of gravitation, based on a foundational paper of Ehlers Pirani and Schild (EPS).All "extended theories of gravitation" (also known as f(R) theories) in Palatini formalism are shown to belong to this class. In a forthcoming paper we shall show that this class of theories contains other more general examples. EPS framework helps in the interpretation and solution of these models that however have exotic behaviours even compared to f(R) theories.
  11/2009;
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  Available from: silvio mercadante

  Article: First Order Extended Gravity and the Dark Side of the Universe: the General Theory

  S. Capozziello, M. De Laurentis, M. Francaviglia, S. Mercadante
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  ABSTRACT: General Relativity is not the definitive theory of Gravitation due to several shortcomings which are coming out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological scales) the attempts to match it with the today observational data lead to invoke Dark Energy and Dark Matter as the bulk components of the cosmic fluid. Since no final evidence, at fundamental level, exists for such ingredients, it is clear that General Relativity presents shortcomings at infrared scales. On the other hand, the attempts to formulate theories more general than the Einstein one give rise to mathematical difficulties that need workarounds which, in turn, generate problems from the interpretative viewpoint. We present here a completely new approach to the mathematical objects in terms of which a theory of Gravitation may be written in a first-order `a la Palatini formalism, and introduce the concept of Dark Metric which could completely bypass the introduction of disturbing concepts as Dark Energy and Dark Matter. Comment: Proceedings of the Conference "The Invisible Universe" Paris, June 29-July 3, 2009 10 pages
  11/2009;
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  Available from: ArXiv

  Article: Global Barbero-Immirzi Connections

  L. Fatibene, M. Francaviglia
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  ABSTRACT: The Barbero-Immirzi (BI) connection, as usually introduced out of a spin connection, is a global object though it does not transform properly as a genuine connection with respect to generic spin transformations, unless quite specific and suitable gauges are imposed. We shall here investigate whether and under which global conditions a (properly transforming and hence global) SU(2)-connection can be canonically defined in a gauge covariant way in such a way that SU(2)-connection locally agrees with the usual BI connection and can be defined on pretty general bundles (in particular triviality is not assumed). As a by-product we shall also introduce a global covariant SU(2)-connection over the whole spacetime (while for technical reasons the BI connection in the standard formulation is just introduced on a space slice) which restricts to the usual BI connection on a space slice. Comment: 9 pages
  05/2009;
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  Available from: ArXiv

  Article: General theory of Lie derivatives for Lorentz tensors

  L. Fatibene, M. Francaviglia
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  ABSTRACT: We show how the ad hoc prescriptions appeared in 2001 by Ortin for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier in 1996 in a much more general setting encompassing older results of Y. Kosmann in 1971. Comment: Typos corrected, references added, some application added. 11 pages
  04/2009;
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  Available from: Salvatore Capozziello

  Article: Stochastic Background of Gravitational Waves as a Benchmark for Extended Theories of Gravity

  S. Capozziello, M. De Laurentis, M. Francaviglia
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  ABSTRACT: The cosmological background of gravitational waves can be tuned by Extended Theories of Gravity. In particular, it can be shown that assuming a generic function f(R) of the Ricci scalar R gives a parametric approach to control the evolution and the production mechanism of gravitational waves in the early Universe.
  12/2008;