Nonsymmetric gravitational theory

Moffat, J. W.

doi:10.1063/1.530993

Cited by 63 publications

(92 citation statements)

References 37 publications

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“…Historically, the firsts theoretical schemes for theories with nonsymmetric metrics and conceptual and heuristic arguments to suit with existing experimental data were proposed in [1,2,3,4,7,8]. That stimulated certain interest of the scientific community (together with more or less motivated criticism) and a lot of discussions how to cure such theories [39,11,40].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…We shall not present detailed proofs if they can be obtained by local computations similar to those presented in [24,25,15,7,8]. The main difference is that in this article we work on nonholonomic manifolds with locally fibred structure defined by the nonlinear connection structure but not on tangent bundles or on usual Riemann-Cartan spaces and their nonsymmetric metric generalizations.…”

Section: Introductionmentioning

confidence: 99%

“…A nonsymmetric gravitational theory (NGT) based on decompositions of the nonsymmetric metricǧ µν and affine connection Γ α βγ was elaborated in series of work by J. Moffat and coauthors, see [5,6,7,8,9,10] and references therein 4 .…”

Section: Nonsymmetric Gravity and Nonholonomic Framesmentioning

confidence: 99%

“…The third step of developments on nonsymmetric theory of gravity can be associated with J. Moffat works [5,6] and further modifications proposed and outlined in [7,8], generalization to noncommutative quantum gravity [9], and applications in modern cosmology [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

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Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics

Vacaru¹

2008

SIGMA

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Abstract. We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart-Moffat and Finsler-Lagrange spaces with connections compatible to a general nonsymmetric metric structure. Elaborating a metrization procedure for arbitrary distinguished connections, we define the class of distinguished linear connections which are compatible with the nonlinear connection and general nonsymmetric metric structures. The nonsymmetric gravity theory is formulated in terms of metric compatible connections. Finally, there are constructed such nonholonomic deformations of geometric structures when the Einstein and/or Lagrange-Finsler manifolds are transformed equivalently into spaces with generic local anisotropy induced by nonsymmetric metrics and generalized connections. We speculate on possible applications of such geometric methods in Einstein and generalized theories of gravity, analogous gravity and geometric mechanics.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Nonsymmetric Gravity and Nonholonomic Framesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics

Vacaru¹

2008

SIGMA

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“…As we pointed out before, various geometrical theories which are alternatives to GR have been put forward since its beginning for explaining the gravitational phenomenon [9,[20][21][22][23][24][25][26]. The conservation law (T µν ;µ = 0) is one of them which does not hold true in a curved space-time in some of these theories.…”

Section: Introductionmentioning

confidence: 99%

Generalized Mattig’s relation in Brans–Dicke–Rastall gravity

Salako

Houndjo

Jawad

2016

Int. J. Mod. Phys. D

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The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector η(z) and observer area distance r0(z) and compare the results with ΛCDM model.

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Nonassociative Geometry of Nonholonomic Phase Spaces with Star R‐flux String Deformations and (non) Symmetric Metrics

Vacaru

Veliev

Bubuianu³

2021

Fortschritte der Physik

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We elaborate on nonassociative differential geometry of phase spaces endowed with nonholonomic (non-integrable) distributions and frames, nonlinear and linear connections, symmetric and nonsymmetric metrics, and correspondingly adapted quasi-Hopf algebra structures. The approach is based on the concept of nonassociative star product introduced for describing closed strings moving in a constant R-flux background. Generalized Moyal-Weyl deformations are considered when, for nonassociative and noncommutative terms of star deformations, there are used nonholonomic frames (bases) instead of local partial derivatives. In such modified nonassociative and nonholonomic spacetimes and associated complex/real phase spaces, the coefficients of geometric and physical objects depend both on base spacetime coordinates and conventional (co) fiber velocity/momentum variables like in (non) commutative Finsler-Lagrange-Hamilton geometry. For nonassociative and (non) commutative phase spaces modelled as total spaces of (co) tangent bundles on Lorentz manifolds enabled with star products and nonholonomic frames, we consider associated nonlinear connection, N-connection, structures determining conventional horizontal and (co) vertical (for instance, 4+4) splitting of dimensions and N-adapted decompositions of fundamental geometric objects. There are defined and computed in abstract geometric and N-adapted coefficient forms the torsion, curvature and Ricci tensors. We extend certain methods of nonholonomic geometry in order to construct R-flux deformations of vacuum Einstein equations for the case of N-adapted linear connections and symmetric and nonsymmetric metric structures. Introduction, Motivations and GoalsWe initialize a research on nonassociative nonholonomic geometry induced by R-flux backgrounds in string gravity and classical and quantum models on phase spaces modelled as (co) tangent Lorentz bundles endowed with nonholonomic (non-integrable, equivalently, anholonomic) structures and nonsymmetric metrics. Such a nonholonomic geometric formalism was elaborated for various types of (non) commutative gravity and matter field theories, modified (relativistic) geometric flows, and classical and quantum information theories, see details in a series of our previous works [1][2][3][4][5][6][7][8][9][10][11] and references therein. In this article, nonassociative geometric and physical models are formulated in a form which is accessible to researchers in particle physics and modern cosmology. There are provided nonholonomic generalizations of two recent models of nonassociative geometry and vacuum gravity due to [12] and, with

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Nonsymmetric gravitational theory

Cited by 63 publications

References 37 publications

Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics

Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics

Generalized Mattig’s relation in Brans–Dicke–Rastall gravity

Nonassociative Geometry of Nonholonomic Phase Spaces with Star R‐flux String Deformations and (non) Symmetric Metrics

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