Finsleroid-regular space: curvature tensor, continuation of gravitational Schwarzschild metric

TL;DR

This paper introduces a method for calculating the curvature tensor of Finsleroid-regular space and extends the Schwarzschild metric into a Finslerian framework, providing a new geometric approach to gravitational fields.

Contribution

It presents a straightforward calculation method for the curvature tensor of Finsleroid-regular space and uniquely extends the Schwarzschild metric into a Finslerian domain.

Findings

Curvature tensor calculation method for Finsleroid-regular space

Extension of Schwarzschild metric into Finslerian geometry

Consistent treatment of the pseudo-Finsleroid axis vector field

Abstract

The method of simple straightforward calculation of the curvature tensor of the Finsleroid--regular space is indicated. The Schwarzschild metric which underlines the gravitational field produced by static spherical-symmetric body is shown to be uniquely extended to the Finslerian domain upon a consistent treatment of the pseudo-Finsleroid axis vector field $b_i$ to be the field of the time variable. Keywords: Finsler metrics, gravitational equations, curvature tensors.