General-relativistic rotation laws in rotating fluid bodies, new weak-field effects and the post-newtonian expansion

TL;DR

This paper extends Newtonian rotation laws into general relativity, revealing new weak-field effects like anti-dragging and deviations from Keplerian motion, with implications for rotating black holes and fluid dynamics.

Contribution

It introduces general-relativistic rotation laws that uncover novel weak-field effects and provides a framework for analyzing rotating fluid bodies in the post-Newtonian regime.

Findings

Revealed anti-dragging effect in rotating tori.

Discovered deviation from Keplerian motion due to selfgravity.

Applied results to black hole parameter inequalities.

Abstract

Recent general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids allow one to rederive, in the first post-Newtonian approximation, the well known geometric dragging of frames, and two new weak-field effects within rotating tori. These are the recently discovered anti-dragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids selfgravity. They can be applied to the study of the existence of the (post-)Newtonian limits of solutions and in investigations of inequalities relating parameters of rotating black holes.