Complementarity of Kinematics and Geometry in General Relativity Theory

TL;DR

This paper explores how kinematic tensors influence the geometry in general relativity, revealing conditions under which geometry is determined by kinematics and discussing foundational principles of geometrization and conventionalism.

Contribution

It demonstrates that kinematic tensors can define spacetime geometry up to a certain arbitrariness when specific integrability conditions are met, linking kinematics with geometric structure.

Findings

Kinematic tensors determine geometry with arbitrariness under certain conditions

Integrability of the spin tensor is crucial for geometry determination

Discussion of geometrization principle and Poincare's conventionalism

Abstract

Relations between kinematics, geometry and law of reference frame motion are considered. We show, that kinematical tensors define geometry up to a space functional arbitrariness when integrability condition for spin tensor is satisfied. Some aspects of geometrization principle and geometrical conventionalism of Poincare are discussed in a light of the obtained results.