Randers<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:mrow></mml:math>-waves

Heefer, Sjors; Pfeifer, Christian; Fuster, Andrea

doi:10.1103/physrevd.104.024007

Cited by 12 publications

(28 citation statements)

References 55 publications

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“…There are a lot of works in the literature studying the space-time consequences of a velocity dependent metric [104][105][106][107][108][109][110], and in particular, in the setting of LIV scenarios [111][112][113][114][115]. Most of them have been developed by considering Finsler geometries, formulated by Finsler in 1918 [116] (these geometries are a generalization of Riemannian spaces where the space-time metric can depend also on vectors of the tangent space).…”

Section: Cotangent Bundle Geometrymentioning

confidence: 99%

Relativistic deformed kinematics: from flat to curved spacetimes

Relancio

2022

Preprint

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Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the Einstenian relativity principle is generalized, adding to the speed of light another relativistic invariant, the Planck energy. There are several papers in the literature showing a connection between this deformed kinematics and a curved momentum space.Here we review how such kinematics can be derived from geometrical ingredients in a rigorous way, and how they can be generalized when regarding a curved spacetime. For the last aim, it is mandatory to consider a particular geometry for all phase-space variables, the so-called generalized Hamilton spaces. This construction allows us to define a spacetime in these theories, which in fact depends on the momenta. Then, starting from such a momentum dependent metric, we also revise several concepts of general relativity, with the final aim of establishing a self-consistent geometrical structure from which quantum gravity phenomenology can be explored.

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Section: Cotangent Bundle Geometrymentioning

confidence: 99%

Relativistic deformed kinematics: from flat to curved spacetimes

Relancio

2022

Preprint

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“…b. Examples of Finsler spacetimes The above definition allows for Finsler spacetimes of: [7], where a is as above and b = b i dx i is a differential 1-form on M. We proved in [43] that, if a ij b i b j ∈ (0, 1) then F provides a Finsler spacetime structure on M. In the context of physics, these geometries are employed to study the motion of an electrically charged particle in an electromagnetic field, the propagation of light in static spacetimes [51], Lorentz violating field theories from the standard model extension [18,52,53] and Finsler gravitational waves [54]. Recently also spinors have been constructed on Randers geometries in terms of Clifford bundles [55].…”

Section: Nx Ox Txmentioning

confidence: 99%

Mathematical foundations for field theories on Finsler spacetimes

Hohmann,

Pfeifer,

Voicu

2021

Preprint

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The paper introduces a general mathematical framework for action based field theories on Finsler spacetimes. As most often fields on Finsler spacetime (e.g., the Finsler fundamental function or the resulting metric tensor) have a homogeneous dependence on the tangent directions of spacetime, we construct the appropriate configuration bundles whose sections are such homogeneous fields; on these configuration bundles, the tools of coordinate free calculus of variations can be consistently applied to obtain field equations. Moreover, we prove that general covariance of natural Finsler field Lagrangians leads to an averaged energy-momentum conservation law which, in the particular case of Lorentzian spacetimes, is equivalent to the usual, pointwise energy-momentum covariant conservation law.

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“…Among all Finsler structures, the class of (α, β)-metrics, obtained by constructing a geometric length measure for curves from a (pseudo)-Riemannian metric a and a 1-form b, are the easiest to construct and the most used in practice. Notorious examples include: Bogoslovsky-Kropina (or m-Kropina) metrics, which represent the framework for VSR and its generalization, very general relativity (VGR) [7,[9][10][11][12] also used for dark energy models [13] -and Randers metrics, used, for instance in the description of propagation of light in static spacetimes [14,15], for the motion of an electrically charged particle in an electromagnetic field, in the study of Finsler gravitational waves [16], or in the SME [15,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

The Finsler spacetime condition for (α,β)-metrics and their isometries

Voicu¹,

Friedl-Szász²,

Popovici-Popescu³

et al. 2023

Preprint

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For the general class of pseudo-Finsler spaces with (α, β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future pointing timelike vectors is ensured. The identified (α, β)-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (α, β)-metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (α, β)-metrics which admit isometries that are not isometries of a.

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Randerspp-waves

Cited by 12 publications

References 55 publications

Relativistic deformed kinematics: from flat to curved spacetimes

Relativistic deformed kinematics: from flat to curved spacetimes

Mathematical foundations for field theories on Finsler spacetimes

The Finsler spacetime condition for (α,β)-metrics and their isometries

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