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

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.