Pseudo-Finsleroid spatial-anisotropic relativistic space

The pseudo-Finsleroid relativistic metric was constructed upon assuming that the involved vector field $b_i$ is time-like. In the present paper it is shown that the metric admits just the alternative counterpart in which the field is space-like. The entailed pseudo-Finsleroid-spatial framework is systematically described. We face on various remarkable properties, including the constant curvature of the associated indicatrix, the explicit Hamiltonian function, transparent presentations for the angle and scalar product. The spray coefficients are found to be of a rather simple structure. The Berwald case is attractively realized. Interesting conformal properties are stemming. {\bf Keywords:} Finsler metrics, relativistic spaces, spray coefficients.