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On variation of action integral in Finsler gravity. (English) Zbl 1414.53069

Summary: In this paper, a generalized action integral of both gravity and matter is defined on the sphere bundle over Finsler space-time manifold \(M\) with a Lorentz-Finsler metric. The Euler-Lagrange equation of this functional, a generalization of the Riemann-Einstein gravity equation is obtained by using some divergence theorems. Fibres of the sphere bundle are unbounded according to the pseudo-Finsler metric. Moreover, solutions of vacuum Finsler gravity equation under the weakly Landsberg condition are discussed and some concrete examples are provided. At last, we raise some questions for further study.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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