Ricci flat Finsler metrics by warped product

TL;DR

This paper introduces a new class of Ricci-flat Finsler metrics constructed via a warped product approach, aligning with static spacetime concepts, and provides explicit examples and PDE characterizations.

Contribution

It proposes a novel warped product framework for Ricci-flat Finsler metrics and constructs explicit non-Riemannian examples, extending previous geometric methods.

Findings

Derived PDE conditions for Ricci-flatness of the new metrics

Constructed two explicit non-Riemannian Ricci-flat Finsler examples

Connected Finsler geometry with static spacetime structures

Abstract

In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen, S. and Zhao (2018), with another "warping", one that is consistent with static spacetimes. We will give the PDE characterization for the proposed metrics to be Ricci-flat and explicitly construct two non-Riemannian examples.