Finsleroid-regular space. Gravitational metric. Berwald case

The Finsleroid-Finsler space proves to become totally regular when the norm ∥b∥ = c of the input 1-form b is taken to be an arbitrary positive scalar c(x) < 1. By performing required direct evaluations, the respective spray coefficients have been obtained in a simple and transparent form. The adequate regular pseudo-Finsleroid metric function is indicated. A convenient method is elaborated to evaluate the associated Finslerian curvature tensor. The (pseudo-)Finsleroid-regular Berwald space is obtainable under the assumptions that the Finsleroid charge is a constant and the 1-form b is parallel. A continuation of the Schwarzschild metric in the Finslerian domain with respect to the parameter g has consistently arisen.