On the metrizability of<i>m</i>-Kropina spaces with closed null one-form

Heefer, Sjors; Pfeifer, Christian; Voorthuizen, Jorn van; Fuster, Andrea

doi:10.1063/5.0130523

Cited by 4 publications

(2 citation statements)

References 45 publications

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“…Finsler geometry consists of a natural metric generalization of Riemannian geometry. During the last years, rapid progress in the field of Finsler geometry and its applications to gravity and cosmology have extended the research in on corresponding topics; some recent works include [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In generalized metric spaces such as Finsler or Finsler-like spacetime, where the motion/velocity/direction are incorporated in the spacetime structure, internal anisotropy inherent in the EDG [27][28][29] and Raychaudhuri equations are attributed on the framework of a tangent bundle of spacetime manifold, thus extending the concept of volume 𝜃, shear 𝜎, and vorticity 𝜔 [30,31].…”

Section: Introductionmentioning

confidence: 99%

Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime

Triantafyllopoulos,

Kapsabelis,

Stavrinos

2024

Universe

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In this article, we study the form of the deviation of geodesics (tidal forces) and the Raychaudhuri equation in a Schwarzschild–Finsler–Randers (SFR) spacetime which has been investigated in previous papers. This model is obtained by considering the structure of a Lorentz tangent bundle of spacetime and, in particular, the kind of the curvatures in generalized metric spaces where there is more than one curvature tensor, such as Finsler-like spacetimes. In these cases, the concept of the Raychaudhuri equation is extended with extra terms and degrees of freedom from the dependence on internal variables such as the velocity or an anisotropic vector field. Additionally, we investigate some consequences of the weak-field limit on the spacetime under consideration and study the Newtonian limit equations which include a generalization of the Poisson equation.

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Section: Introductionmentioning

confidence: 99%

Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime

Triantafyllopoulos,

Kapsabelis,

Stavrinos

2024

Universe

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“…To this aim, we first find, in Theorem 3, the necessary and sufficient conditions for the pseudo-Riemann metrizability of a given SO(3)-invariant non-Riemannian Berwald-Finsler structure: the symmetry of the connection Ricci tensor (which was known [12,15,16], to be necessary), together with a non-maximal dimension of the vertical part of the corresponding holonomy algebra. These two conditions are independent, as proven by concrete examples.…”

Section: Introductionmentioning

confidence: 99%

Metrizability of S O ( 3 ) -invariant connections: Riemann versu

Voicu,

Elgendi

2024

Class. Quantum Grav.

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For a torsion-free affine connection on a given manifold, which does not necessarily arise as the Levi-Civita connection of any pseudo-Riemannian metric, it is still possible that it corresponds in a canonical way to a Finsler structure; this property is known as Finsler (or Berwald-Finsler) metrizability.In the present paper, we clarify, for 4-dimensional SO(3)-invariant, Berwald-Finsler metrizable connections, the issue of the existence of an affinely equivalent pseudo-Riemannian structure. In particular, we find all classes of SO (3)-invariant connections which are not Levi-Civita connections for any pseudo-Riemannian metric - hence, are non-metric in a conventional way - but can still be metrized by SO(3)-invariant Finsler functions. The implications for physics, together with some examples are briefly discussed.

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Berwald m-Kropina spaces of arbitrary signature: Metrizability and Ricci-flatness

Heefer

2024

Journal of Mathematical Physics

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The (pseudo-)Riemann-metrizability and Ricci-flatness of Finsler spaces with m-Kropina metric F = α1+mβ−m of Berwald type are investigated. We prove that the affine connection of F can locally be understood as the Levi–Civita connection of some (pseudo-)Riemannian metric if and only if the Ricci tensor of the canonical affine connection is symmetric. We also obtain a third equivalent characterization in terms of the covariant derivative of the 1-form β. We use these results to classify all locally metrizable m-Kropina spaces whose 1-forms have a constant causal character. In the special case where the first de Rham cohomology group of the underlying manifold is trivial (which is true of simply connected manifolds, for instance), we show that global metrizability is equivalent to local metrizability and hence, in that case, our necessary and sufficient conditions also characterize global metrizability. In addition, we further obtain explicitly all Ricci-flat, locally metrizable m-Kropina metrics in (3 + 1)D whose 1-forms have a constant causal character. In fact, the only possibilities are essentially the following two: either α is flat and β is α-parallel, or α is a pp-wave and β is α-parallel.

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On the metrizability ofm-Kropina spaces with closed null one-form

Cited by 4 publications

References 45 publications

Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime

Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime

Metrizability of S O ( 3 ) -invariant connections: Riemann versu

Berwald m-Kropina spaces of arbitrary signature: Metrizability and Ricci-flatness

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