Rotation and pseudo-rotation

TL;DR

This paper explores the concepts of rotation and pseudo-rotation of eigenvector-based bases in space-times, analyzing their implications for metric properties, sources, and symmetries within Einstein's framework.

Contribution

It introduces the notion of pseudo-rotation for spacelike eigenvector congruences and examines their role alongside true rotation in space-time descriptions.

Findings

Eigenvectors of stress-energy tensor form privileged bases.

Pseudo-rotation extends the concept of rotation to spacelike congruences.

Implications for metric properties and space-time symmetries are discussed.

Abstract

Eigenvectors of stress-energy tensor (the source in Einstein's equations) form privileged bases in description of the corresponding space-times. When one or more of these vector fields are rotating (the property well determined in differential geometry), one says that the space-time executes this rotation. Though the rotation in its proper sense is understood as that of a timelike congruence (vector field), the rotation of a spacelike congruence is not a less objective property if it corresponds to a canonical proper basis built of the just mentioned eigenvectors. In this last case, we propose to speak on pseudo-rotation. Both properties of metric, its material sources, and space-time symmetries are considered in this paper.