TY - JOUR

T1 - On the metrizability of m -Kropina spaces with closed null one-form

AU - Heefer, Sjors

AU - Pfeifer, Christian

AU - Van Voorthuizen, Jorn

AU - Fuster, Andrea

N1 - Funding Information: C.P. was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Project No. 420243324 and acknowledges support from cluster of excellence Quantum Frontiers funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967. All of us would like to acknowledge networking support provided by the COST Action CA18108, supported by COST (European Cooperation in Science and Technology).

PY - 2023/2/1

Y1 - 2023/2/1

N2 - We investigate the local metrizability of Finsler spaces with m-Kropina metric F = α1+mβ-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.

AB - We investigate the local metrizability of Finsler spaces with m-Kropina metric F = α1+mβ-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.

UR - http://www.scopus.com/inward/record.url?scp=85147800800&partnerID=8YFLogxK

U2 - 10.1063/5.0130523

DO - 10.1063/5.0130523

M3 - Article

AN - SCOPUS:85147800800

VL - 64

JO - Journal of mathematical physics

JF - Journal of mathematical physics

SN - 0022-2488

IS - 2

M1 - 022502

ER -