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

Samira Cheraghchi

Department of Mathematics and Computer Science, Transilvania University, 50, Iuliu Maniu str., 500091 Brasov, Romania

E-mail Address: [email protected]

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Christian Pfeifer

ZARM, University of Bremen, Am Fallturm 2, 28359 Bremen, Germany

E-mail Address: [email protected]

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, and

Nicoleta Voicu

https://orcid.org/0000-0001-9263-2379

Department of Mathematics and Computer Science, Transilvania University, 50, Iuliu Maniu str., 500091 Brasov, Romania

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0219887823501906Cited by:2 (Source: Crossref)

Abstract

We locally classify all $SO (3)$ -invariant four-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which are closest to (spatially, or $SO (3)$ )-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) $SO (3)$ -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.

Keywords:

AMSC: 83A05, 53B40, 83C99

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