3,868 research outputs found

    Introductory lectures to loop quantum gravity

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    We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.Comment: Based on lectures given at the 3eme Ecole de Physique Theorique de Jijel, Algeria, 26 Sep -- 3 Oct, 2009. 52 pages, many figures. v2 minor corrections. To be published in the proceeding

    Bi-gravity with a single graviton

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    We analyze a bi-gravity model based on the first order formalism, having as fundamental variables two tetrads but only one Lorentz connection. We show that on a large class of backgrounds its linearization agrees with general relativity. At the non-linear level, additional degrees of freedom appear, and we reveal the mechanism hiding them around the special backgrounds. We further argue that they do not contain a massive graviton, nor the Boulware-Deser ghost. The model thus propagates only one graviton, whereas the nature of the additional degrees of freedom remains to be investigated. We also present a foliation-preserving deformation of the model, which keeps all symmetries except time diffeomorphisms and has three degrees of freedom.Comment: 29 page

    A note on the Plebanski action with cosmological constant and an Immirzi parameter

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    We study the field equations of the Plebanski action for general relativity when both the cosmological constant and an Immirzi parameter are present. We show that the Lagrange multiplier, which usually gets identified with the Weyl curvature, now acquires a trace part. Some consequences of this for a class of modified gravity theories recently proposed in the literature are briefly discussed.Comment: 14 pages. v2: factor 2 corrected, updated reference

    Null twisted geometries

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    We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper action-angle variables on the gauge-invariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantise the phase space and its algebra using Dirac's algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labelled by SO(2) quantum numbers, and are embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group.Comment: 22 pages, 3 figures. v2: minor corrections, improved presentation in section 4, references update

    On the Relations between Gravity and BF Theories

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    We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.Comment: v3: journal typeset versio

    On helicity fluctuations and the energy cascade in turbulence

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    Recent conjectures concerning the correlation between regions of high local helicity and low dissipation are examined from a rigorous theoretical standpoint based on the Navier-Stokes equations. It is proven that only the solenoidal part of the Lamb vector omega x u (which is directly tied to the nonlocal convection and stretching of vortex lines) contributes to the energy cascade in turbulence. Consequently, it is shown that regions of low dissipation can be associated with either low or high helicity, a result which disproves earlier speculations concerning this direct connection between helicity and the energy cascade. Some brief examples are given along with a discussion of the consistency of these results with the most recent computations of helicity fluctuations in incompressible turbulent flows

    On the advantages of the vorticity-velocity formulation of the equations of fluid dynamics

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    The mathematical properties of the pressure-velocity and vorticity-velocity formulations of the equations of viscous flow are compared. It is shown that a vorticity-velocity formulation exists which has the interesting property that non-inertial effects only enter the problem through the implementation of initial and boundary conditions. This valuable characteristic, along with other advantages of the vorticity-velocity approach, are discussed in detail

    On the freestream matching condition for stagnation point turbulent flows

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    The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises from the standard kappa-epsilon model is not due to a defect in the model but results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production equals dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain - a turbulent flow which does not reach such a simple equilibrium. Consequently, the adjustment that has been made in the constants of the epsilon-transport equation to eliminate this singularity is not self-consistent since it is tantamount to artificially imposing an equilibrium structure on a turbulent flow which is known not to have one

    Coherent structures

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    In order to develop more quantitative measures of coherent structures that would have comparative value over a range of experiments, it is essential that such measures be independent of the observer. It is only through such a general framework that theories with a fundamental predictive value can be developed. The triple decomposition phi = bar-phi + phi(c) + phi(r) (where bar-phi is the mean, phi(c) is the coherent part, and phi(r) is the random part of any turbulent field phi) serves this purpose. The equations of motion for the mean and coherent flow fields, based on the triple decomposition, are presented and modeling methods for the time-averaged and phase-averaged Reynolds stress are discussed

    Discussion of turbulence modelling: Past and future

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    The full text of a paper presented at the Whither Turbulence Workshop (Cornell University, March 22-24, 1989) on past and future trends in turbulence modeling is provided. It is argued that Reynolds stress models are likely to remain the preferred approach for technological applications for at least the next few decades. In general agreement with the Launder position paper, it is further argued that among the variety of Reynolds stress models in use, second-order closures constitute by far the most promising approach. However, some needed improvements in the specification of the turbulent length scale are emphasized. The central points of the paper are illustrated by examples from homogeneous turbulence
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