Finsler spacetime in light of Segal’s principle

Dhasmana, Shailesh; Силагадзе, З. К.

doi:10.1142/s0217732320500194

Cited by 7 publications

(4 citation statements)

References 38 publications

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“…The symmetry of the Bogoslovsky-Finsler model is in fact of the Very Special Relativity (VRS) type ; in the Minkowski case it is the 8-parameter DISIM b (2) [7,33,38]. The clue is to deform an u-v boost N 0 to N b in as (V.8).…”

Section: Discussionmentioning

confidence: 99%

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Geodesic motion in Bogoslovsky-Finsler Spacetimes

Elbistan,

Zhang,

Dimakis

et al. 2020

Preprint

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We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitational wave in Einstein's General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a certain deformation of Cohen and Glashow's Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gravitational wave for any value of the Bogoslovsky-Finsler parameter b. We then replace the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaître model.

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Section: Discussionmentioning

confidence: 99%

“…For a review of these ideas and their relation to much earlier work of Voigt [31], the reader is directed to the recent review [32]. For a recent discussion of Bogoslovsky-Finsler deformations in the light of ideas of Segal see [33].…”

Section: Bogoslovsky-finsler Metricsmentioning

confidence: 99%

Geodesic motion in Bogoslovsky-Finsler Spacetimes

Elbistan,

Zhang,

Dimakis

et al. 2020

Preprint

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“…where n µ is a fixed null vector. Therefore, according to Segal's principle, we can expect that b is not zero, but it can be extremely small by analogy with the cosmological constant [24]. The unit vector n in n µ = (1, n) indicates the preferred direction in three-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

On Finslerian extension of special relativity

Sagaydak,

Silagadze

2022

Preprint

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We demonstrate that Robb-Geroch's definition of a relativistic interval admits a simple and fairly natural generalization leading to a Finsler extension of special relativity. Another justification for such an extension goes back to the works of Lalan and Alway and, finally, was put on a solid basis and systematically investigated by Bogoslovsky under the name "Special-relativistic theory of locally anisotropic space-time". The isometry group of this space-time, DISIM b (2), is a deformation of the Cohen and Glashow's very special relativity symmetry group ISIM(2). Thus, the deformation parameter b can be regarded as an analog of the cosmological constant characterizing the deformation of the Poincaré group into the de Sitter (anti-de Sitter) group. The simplicity and naturalness of Finslerian extension in the context of this article adds weight to the argument that the possibility of a nonzero value of b should be carefully considered.

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“…Of course, when the parameter b is zero the typical pseudo-Riemannian line-element of special relativity is recovered. The b → 0 limit however is quite subtle at the level of the finite symmetry transformations since the preferred direction introduced with ℓ in (1) persists in those relations (see [13]).…”

Section: Introductionmentioning

confidence: 99%

Hidden Symmetries in Deformed Very Special Relativity

Dimakis

2021

Preprint

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We study particle dynamics in a space-time invariant under the DISIM b (2) group -the deformation of the ISIM (2) symmetry group of very special relativity. We find that the Lorentz violation leads to the creation of higher order (hidden) symmetries which are connected to those broken at the space-time level. Through the perspective of the conserved quantities of the special relativistic case the Lorentz violation is linked to specific non-commutative relations in phase-space.

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Finsler spacetime in light of Segal’s principle

Cited by 7 publications

References 38 publications

Geodesic motion in Bogoslovsky-Finsler Spacetimes

Geodesic motion in Bogoslovsky-Finsler Spacetimes

On Finslerian extension of special relativity

Hidden Symmetries in Deformed Very Special Relativity

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