Pseudo-Finsleroid spatial-anisotropic relativistic space

TL;DR

This paper explores an alternative pseudo-Finsleroid relativistic space with a space-like vector field, detailing its geometric properties, Hamiltonian, and conformal features, expanding the understanding of anisotropic relativistic metrics.

Contribution

It introduces and systematically describes a space-like vector field version of the pseudo-Finsleroid metric, highlighting its geometric and conformal properties, and providing explicit formulas and structures.

Findings

The metric admits a space-like vector field counterpart.

The associated indicatrix has constant curvature.

The spray coefficients have a simple structure.

Abstract

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.