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In this article, we identify precise conditions under which the scalar Finsler gravity vacuum equation (in either its purely metric or its Palatini formulation) reduces to the vanishing of the Finslerian Ricci curvature. Through analytic arguments, we find that this happens if there exists some power $F^n$ of the Finsler function $F$ that is sufficiently regular and whose associated Finsler metric is non-degenerate on the light cones. Moreover, the Landsberg term in the scalar equation must vanish. This result significantly generalizes the findings of [Villasenor2024], where a reduction theorem was established under the quite strong assumption that $F^2$ is regular, which is not satisfied by many examples currently under consideration.
We demonstrate the impact of our findings by applying them to solve the Finsler gravity equations for homogeneous and isotropic Finsler spacetime functions of Landsberg type.
From: Christian Pfeifer [view email]
[v1]
Tue, 23 Jun 2026 15:25:23 UTC (35 KB)
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