On the Analyticity of Static Solutions of a Field Equation in Finsler Gravity

Erasmo Caponio,Antonio Masiello

doi:10.3390/universe6040059

Abstract

It is well-known that static vacuum solutions of Einstein equations are analytic in suitable coordinates. We ask here for an extension of this result in the context of Finsler gravity. We consider Finsler spacetimes that retain several properties of static Lorentzian spacetimes, are Berwald and have vanishing Ricci scalar.

Highlights

In a couple of papers appeared in 1970 [1,2], H
Our aim in this paper is to investigate if this result can be extended to static Finsler spacetimes of Berwald type
Let us recall the notion of a Killing vector field for a Finsler metric

Summary

Introduction

In a couple of papers appeared in 1970 [1,2], H. Müller zum Hagen proved that on any C3 static or stationary spacetime which is a vacuum solution of the Einstein equations there exists an appropriate analytic atlas such that the metric coefficients of the solution are analytic. Our aim in this paper is to investigate if this result can be extended to static Finsler spacetimes of Berwald type. This goal forces us to analyse at least three questions: What is the convenient definition of a Finsler spacetime?. We will consider each of the above questions in the three sections.

On the Definition of a Finsler Spacetime

About the Notion of Stationary and Static Finsler Spacetimes

Vacuum Field Equations

On the Analyticity of the Average Metric of a Static Berwald Solution

Conclusions