General-relativistic rotation laws in rotating fluid bodies

TL;DR

This paper develops new general-relativistic rotation laws for rotating fluids, deriving effects like frame dragging, anti-dragging, and deviations from Keplerian motion, enhancing understanding of relativistic rotating bodies.

Contribution

It introduces novel general-relativistic rotation laws and derives new weak-field effects, advancing the modeling of rotating fluid bodies in general relativity.

Findings

Re-derivation of frame dragging in the first post-Newtonian approximation

Identification of dynamic anti-dragging effect in rotating tori

Discovery of a new effect measuring deviations from Keplerian motion

Abstract

We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to re-derive, in the first post-Newtonian approximation, the well known geometric dragging of frames. We derive two other general-relativistic weak-field effects within rotating tori: the recently discovered dynamic anti-dragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids selfgravity. One can use the rotation laws to study the uniqueness and the convergence of the post-Newtonian approximations, and the existence of the post-Newtonian limits.