On the Fundamental Equations of Electromagnetism in Finslerian Spacetimes

Voicu, Nicoleta

doi:10.2528/pier10122108

Cited by 15 publications

(12 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This construction refines the one in [20]. With this, we get one more property of the connections α D :…”

Section: Introductionmentioning

confidence: 56%

On a new unified geometric description of gravity and electromagnetism

Voicu¹

2011

Preprint

Self Cite

View full text Add to dashboard Cite

In a previous paper, we have introduced a new unified description of the main equations of the gravitational and of the electromagnetic field, in terms of tidal tensors and connections on the tangent bundle T M of the space-time manifold. In the present work, we relate these equations to variational procedures on the tangent bundle. The Ricci scalar of the proposed connection is dynamically equivalent to the usual Einstein-Maxwell Lagrangian. Also, in order to be able to perform these variational procedures, we find an appropriate completion of the metric tensor (from the base manifold) up to a metric structure on T M.

show abstract

“…This construction refines the one in [20]. With this, we get one more property of the connections α D :…”

Section: Introductionmentioning

confidence: 56%

On a new unified geometric description of gravity and electromagnetism

Voicu¹

2011

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Previous studies that incorporate the electromagnetic field tensor and the associated Maxwell equations in the framework of the metric tangent bundle have been made, for example in [2,10,36,67,68].…”

Section: Electromagnetic Field Tensormentioning

confidence: 99%

“…This can be physically described in the framework of Finsler-like geometrical structure of spacetime. Einstein Finsler-like gravity theories are considered as natural candidates for investigation of local anisotropies and the dark energy problem [1,5,7,21,[34][35][36][37][38]. Also, extended modified gravity theories in the framework of tangent Lorentz bundles allow generalizations of the f (R, T, .…”

Section: Introductionmentioning

confidence: 99%

Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

Triantafyllopoulos

Stavrinos

2018

Class. Quantum Grav.

View full text Add to dashboard Cite

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of General Relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4−velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein-Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.

show abstract

“…The necessity of devising such a model has been always evident, and the main criterion of its validity is a physically consistent geometric description of classical fields. Investigations in this area from the very first works on the gravitational field geometry [1][2][3] and early attempts of electrodynamics geometrization [4][5][6] up to the present-day studies [7][8][9], provided a desired model with at least two critical restrictions.…”

Section: Introductionmentioning

confidence: 99%

Model of Embedded Spaces: Gravitation and electricity

Noskov

2016

Gravit. Cosmol.

View full text Add to dashboard Cite

Simultaneous non-configuration geometrization of classical electrodynamics and gravity leads to a 4D space which refer to the Model of Embedded Spaces (MES). MES presupposes the existence of their own space (manifold) in any massive particle (element of matter distribution) and argues that spacetime of the universe is the 4D metric result of dynamical embedding of proper manifolds, whose partial contribution is determined by matter interactions. The resulting space is equipped with Riemann-like geometry, whose differential formalism, in a test particle approximation, is obtained by a formal change of the gradient operator ∂/∂x i → ∂/∂x i + 2u k ∂ 2 /∂x [i ∂u k] , where u i = dx i /ds is the velocity of matter. In this paper the features of the geometry of dynamical embedding are analyzed, and MES analogs of the Einstein and Maxwell equations are obtained. It has been shown that the electric charge is a direct consequence of the gravitational constant and inertial mass of matter. We also discuss some fundamental physical and cosmological aspects of the developed ideas.

show abstract

On the Fundamental Equations of Electromagnetism in Finslerian Spacetimes

Cited by 15 publications

References 23 publications

On a new unified geometric description of gravity and electromagnetism

On a new unified geometric description of gravity and electromagnetism

Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

Model of Embedded Spaces: Gravitation and electricity

Contact Info

Product

Resources

About