Finsler pp-waves and the Penrose limit

We investigate the local metrizability of Finsler spaces with m-Kropina metric F = α1+ m β− m, where β is a closed null one-form. We show that such a space is of Berwald type if and only if the (pseudo-)Riemannian metric α and one-form β have a very specific form in certain coordinates. In particular, when the signature of α is Lorentzian, α belongs to a certain subclass of the Kundt class and β generates the corresponding null congruence, and this generalizes in a natural way to arbitrary signature. We use this result to prove that the affine connection on such an m-Kropina space is locally metrizable by a (pseudo-)Riemannian metric if and only if the Ricci tensor constructed from the affine connection is symmetric. In particular, we construct all counterexamples of this type to Szabo’s metrization theorem, which has only been proven for positive definite Finsler metrics that are regular on all of the slit tangent bundle.

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

Heefer

Pfeifer

Voorthuizen

et al. 2023

Journal of Mathematical Physics

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Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces

Cheraghchi

Pfeifer

Voicu

2023

Int. J. Geom. Methods Mod. Phys.

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We locally classify all [Formula: see text]-invariant four-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which are closest to (spatially, or [Formula: see text])-spherically symmetric pseudo-Riemannian ones — and serve as ansatz to find solutions of Finsler gravity equations which generalize the Einstein equations. We find that there exist five classes of non-pseudo-Riemannian (i.e. non-quadratic in the velocities) [Formula: see text]-spherically symmetric pseudo-Finsler Berwald functions, which have either a heavily constrained dependence on the velocities, or, up to a suitable choice of the tangent bundle coordinates, no dependence at all on the “time” and “radial” coordinates.

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Finsler pp-waves and the Penrose limit

Cited by 2 publications

References 38 publications

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

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

Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces

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