Noncommutative deformation of four-dimensional Einstein gravity

Cardella, Matteo A.; Zanon, D.

doi:10.1088/0264-9381/20/8/101

Cited by 69 publications

(88 citation statements)

References 18 publications

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“…This model with the gauge symmetries intact was generalized to NC spacetime (via the * -product and the SeibergWitten map) but it turned out that due to symmetry requirements the O(θ ) corrections miraculously cancel and hence to first order in θ the Einstein action and its NC extension are identical [70][71][72][73][74][75]. Thus we come to the conclusion that symmetries of canonical noncommutative spacetime naturally lead to the noncommutative version of unimodular gravity for O(θ ) results.…”

Section: Cosmological Implicationsmentioning

confidence: 90%

Noncommutative geometry and fluid dynamics

Das

Ghosh

2016

Eur. Phys. J. C

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In the present paper we have developed a NonCommutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the FriedmannRobertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation.

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Section: Cosmological Implicationsmentioning

confidence: 90%

Noncommutative geometry and fluid dynamics

Das

Ghosh

2016

Eur. Phys. J. C

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“…They should be consistent with the quotienting (8), as well as the unimodilarity condition and, of course, the Jacobi identity. For convenience we write the SL(2, R) matrix as…”

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confidence: 54%

“…The region III is then absent in this case. ‡ On the other hand, the Poisson brackets (20) and (21) are undefined in the extremum case J = M ℓ, or r + = r − , for finite coefficients ‡ Zero angular momentum also allows for Poisson brackets which are linear with respect to the four dimensional embedding coordinates and consistent with (8). This will be discussed in a later article.…”

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confidence: 99%

Noncommutative BTZ black hole and discrete time

Dolan

Gupta

Stern

2007

Class. Quantum Grav.

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We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values for the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to R × S 1 symplectic leaves, where R is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator.

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“…[5,6,7,8]; we will here point out the main differences. A careful reader has already noticed that the noncommutative frame formalism has intrinsically geometric formulation.…”

Section: Discussionmentioning

confidence: 94%

WKB Approximation in Noncommutative Gravity

Burić

Madore

Zoupanos

2007

SIGMA

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Abstract. We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the highfrequency waves on the flat background.Key words: noncommutative geometry; models of quantum gravity 2000 Mathematics Subject Classification: 46L87; 83C35 Preliminary formalismOur purpose in this paper is to analyze the relation which exists between the noncommutativity of the local coordinates and the gravitational field on a given space-time. In particular model of noncommutative gravity which we develop, in the noncommutative frame formalism, this relation is expressed as consistency between the algebraic and the differential-geometric structures, or in other language as generalized Jacobi identities.Let µ be a typical 'large' source mass with 'Schwarzschild radius' G N µ. We have two length scales, determined by respectively G N , the square of the Planck length and byk, the scale of noncommutativity. The gravitational field is weak if the dimensionless parameter GF = G N −1 µ 2 is small; the space-time is almost commutative if the dimensionless parameter =kµ 2 is small. These two parameters are not necessarily related but we shall here assume that they are of the same order of magnitude,If noncommutativity is not directly related to gravity then it makes sense to speak of ordinary gravity as the limitk → 0 with G N µ nonvanishing. On the other hand if noncommutativity and gravity are directly related then both should vanish withk. We wish here to consider an expansion in the parameter , which we have seen is a measure of the relative dimension of a typical 'space-time cell' compared with the Planck length of a typical quantity of gravitational energy. Our motivation for considering noncommutative geometry as an 'avatar' of gravity is the belief that it sheds light on the role of the gravitational field as the universal regulator of ultra-violet divergences. We mention here only some elements of the approach we use to This paper is a contribution to the

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Noncommutative deformation of four-dimensional Einstein gravity

Cited by 69 publications

References 18 publications

Noncommutative geometry and fluid dynamics

Noncommutative geometry and fluid dynamics

Noncommutative BTZ black hole and discrete time

WKB Approximation in Noncommutative Gravity

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