Deformed relativity symmetries and the local structure of spacetime

Letizia, Marco; Liberati, Stefano

doi:10.1103/physrevd.95.046007

Cited by 38 publications

(46 citation statements)

References 40 publications

(84 reference statements)

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“…ǫ = 0, F ǫ is a 1-homogeneous Finsler function, for massless particles F 0 must not necessarily be 1-homogeneous. The transition from a dispersion relation to a Finslerian geometry has been worked out explicitly for Planck scale modified dispersion relations [2,38] and for weakly premetric electrodynamics [25]. Depending on the Hamiltonian from which one starts a huge variety of Finsler functions can be obtained.…”

Section: A Duals Of Dispersion Relationsmentioning

confidence: 99%

Finsler spacetime geometry in physics

Pfeifer

2019

Int. J. Geom. Methods Mod. Phys.

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Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general geometric clock and as geometry being compatible with the relevant Ehlers-Pirani-Schild axioms. As Finsler geometry is a straightforward generalisation of Riemannian geometry there are many attempts to use it as generalized geometry of spacetime in physics. However, this generalisation is subtle due to the existence of non-trivial null directions. I review how a pseudo-Finsler spacetime geometry can be defined such that it provides a precise notion of causal curves, observers and their measurements as well as a gravitational field equation determining the Finslerian spacetime geometry dynamically. The construction of such Finsler spacetimes lays they foundation for comparing their predictions with observations, in astrophysics as well as in laboratory experiments. * christian.pfeifer@ut.ee

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Section: A Duals Of Dispersion Relationsmentioning

confidence: 99%

Finsler spacetime geometry in physics

Pfeifer

2019

Int. J. Geom. Methods Mod. Phys.

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“…In the DSR framework, Finsler spacetimes have been studied for flat spacetime [32,33], and also for curved spacetimes [34]. In those papers it was shown that a deformed dispersion relation produce a velocity dependence on the metric.…”

Section: Introductionmentioning

confidence: 99%

Phenomenological consequences of a geometry in the cotangent bundle

Relancio

Liberati

2020

Phys. Rev. D

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A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved momentum space. In this paper, we will discuss a possible generalization to take into account both curvatures and some possible observable effects. We will first explain how to construct a metric in the cotangent bundle in order to have a curved spacetime with a nontrivial geometry in momentum space and the relationship with an action in phase space characterized by a deformed Casimir. Then, we will study within this proposal two different space-time geometries. In the Friedmann-Robertson-Walker universe, we will see the modifications in the geodesics (redshift, luminosity distance and geodesic expansion) due to a momentum dependence of the metric in the cotangent bundle. Also, we will see that when the spacetime considered is a Schwarzschild black hole, one still has a common horizon for particles with different energies, differently from a Lorentz invariance violation case. However, the surface gravity computed as the peeling off of null geodesics is energy dependent. * relancio@unizar.es,liberati@sissa.it 1 See however [14] for an alternative scenario.

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“…Examples are premetric electrodynamics [11] describing among other systems the electromagnetic field in crystals [12] or wave equations in solids [13] which can be used to model earthquake waves [14]. Moreover MDRs are used as an effective description of quantum gravity effects [15][16][17][18], making spacetime effectively a medium whose origin lies in the four momentum dependent scattering of elementary particles with the graviton. More fundamentally MDRs emerge from field theories which break local Lorentz invariance [19], as studied in the standard model extension [20], very special and very general relativity [21][22][23] or again in premetric resp.…”

Section: Introductionmentioning

confidence: 99%

Finsler gravity action from variational completion

2019

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In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be a scalar equation. In the literature two such equations have been suggested: the one by Rutz and the one by one of the authors. Here we employ the method of canonical variational completion to show that Rutz equation can not be obtained from a variation of an action and that its variational completion yields the latter field equations. Moreover, to improve the mathematical rigor in the derivation of the Finsler gravity field equation, we formulate the Finsler gravity action on the positive projective tangent bundle. This has the advantage of allowing us to apply the classical variational principle, by choosing the domains of integration to be compact and independent of the dynamical variable. In particular in the pseudo-Riemannian case, the vacuum field equation becomes equivalent to the vanishing of the Ricci tensor. * manuel.hohmann@ut.ee † christian.pfeifer@ut.ee ‡ nico.voicu@unitbv.ro arXiv:1812.11161v3 [gr-qc] 1 Oct 2019 3 The ones considered in [44,45] do not fit in our definition. We do not consider these Finsler spacetimes since for them the curvature tensor, which defines the dynamics of Finsler spacetimes, is not necessarily defined for all physical observer directions, which in our definition is given by the conic subbundle T . The definition could be relaxed so as to include the possibility of having an observer direction where curvature is not defined, but in this case, a thorough analysis of whether the evolution of spacetime is causal, as seen by the respective observer, is needed. This is the subject for future work.

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Deformed relativity symmetries and the local structure of spacetime

Cited by 38 publications

References 40 publications

Finsler spacetime geometry in physics

Finsler spacetime geometry in physics

Phenomenological consequences of a geometry in the cotangent bundle

Finsler gravity action from variational completion

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