Geometrical Models of the Locally Anisotropic Space-Time

Balan, Vladimir; Bogoslovsky, G. Yu.; Kokarev, Sergey S.; Pavlov, D. G.; Siparov, Sergey; Voicu, Nicoleta

doi:10.4236/jmp.2012.329170

Cited by 20 publications

(30 citation statements)

References 61 publications

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“…Consider, on M = R 4 , a sign-adjusted version of the Berwald-Moor quartic Finslerian metric, [6]: L = sgn(y 0 y 1 y 2 y 3 ) |y 0 y 1 y 2 y 3 |.…”

Section: Berwald-moor Metricmentioning

confidence: 99%

“…Finsler spaces represent a natural geometric framework for applications in physics and biology. Among these, field-theoretical applications have a peculiar importance and are the most numerous (just a few examples: [1], [3], [6], [11], [12], [13], [14], [15], [18], [20], [21]). But, these applications generally require metrics to be of Lorentzian signature.…”

Section: Introductionmentioning

confidence: 99%

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Volume forms for time orientable Finsler spacetimes

Voicu

2017

Journal of Geometry and Physics

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The paper proposes extensions of the notions of Busemann-Hausdorff and Holmes-Thompson volume to time orientable Finslerian spacetime manifolds.These notions are designed to also make sense in cases when the Finslerian metric tensors are either not defined or degenerate along some directions in each tangent space -which is the case with the majority of Lorentzian Finsler metrics used in applications. This feature makes it possible to build well-defined field-theoretical integrals having such metrics as a background.

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“…Consider, on M = R 4 , a sign-adjusted version of the Berwald-Moor quartic Finslerian metric, [6]: L = sgn(y 0 y 1 y 2 y 3 ) |y 0 y 1 y 2 y 3 |.…”

Section: Berwald-moor Metricmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Volume forms for time orientable Finsler spacetimes

Voicu

2017

Journal of Geometry and Physics

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“…There exist several approaches to this transition in the literature. In [8], for example, the Minkowski metric was replaced by a non-flat Lorentzian metric satisfying Einstein's equations and the constant 1-form n was generalized to a 1-form n a (x)dx a satisfying a Klein-Gordon-like equation. This procedure constructs the curved version of the VSR line element from different dynamical fields on spacetime.…”

Section: Introductionmentioning

confidence: 99%

Berwald spacetimes and very special relativity

2018

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In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relativity (VSR) line element, to which we refer as very general relativity (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR spacetime.

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“…This Lagrangian was also considered by Berwald and Moór [7,46] and it has been investigated in several mathematical and physical works, e.g. [2,4,5,36,47]. Bogoslovsky and Goenner [10,11] considered the next Lagrangian (for the physical case n = 3) to which they arrived through symmetry considerations unrelated to the theory of affine spheres…”

Section: The Tetrahedral Anisotropic Theorymentioning

confidence: 99%

Affine sphere spacetimes which satisfy the relativity principle

Minguzzi

2017

Phys. Rev. D

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In the context of Lorentz-Finsler spacetime theories the relativity principle holds at a spacetime point if the indicatrix (observer space) is homogeneous. We point out that in four spacetime dimensions there are just three kinematical models which respect an exact form of the relativity principle and for which all observers agree on the spacetime volume. They have necessarily affine sphere indicatrices. For them every observer which looks at a flash of light emitted by a point would observe, respectively, an expanding (a) sphere, (b) tetrahedron, or (c) cone, with barycenter at the point. The first model corresponds to Lorentzian relativity, the second one has been studied by several authors though the relationship with affine spheres passed unnoticed, and the last one has not been previously recognized and it is studied here in some detail. The symmetry groups are O + (3, 1), R 3 , O + (2, 1) × R, respectively. In the second part, devoted to the general relativistic theory, we show that the field equations can be obtained by gauging the Finsler Lagrangian symmetry while avoiding direct use of Finslerian curvatures. We construct some notable affine sphere spacetimes which in the appropriate velocity limit return the Schwarzschild, Kerr-Schild, Kerr-de Sitter, Kerr-Newman, Taub, and FLRW spacetimes, respectively. CONTENTS

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Geometrical Models of the Locally Anisotropic Space-Time

Cited by 20 publications

References 61 publications

Volume forms for time orientable Finsler spacetimes

Volume forms for time orientable Finsler spacetimes

Berwald spacetimes and very special relativity

Affine sphere spacetimes which satisfy the relativity principle

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