General-relativistic versus Newtonian: geometric dragging and dynamic anti-dragging in stationary disks in the first post-Newtonian approximation

TL;DR

This paper investigates how general relativity influences the rotation of stationary accretion disks around black holes within the first post-Newtonian approximation, revealing both known and new effects on disk dynamics.

Contribution

It identifies a new dynamic anti-dragging effect in addition to the known geometric frame dragging, showing how these effects alter rotation curves in relativistic accretion disks.

Findings

Geometric frame dragging accelerates disk rotation.

A previously unknown dynamic anti-dragging decelerates rotation.

Effects are nonlinear and vanish for test fluids.

Abstract

We evaluate general-relativistic effects in motion of stationary accretion disks around a Schwarzschild black hole, assuming the first post-Newtonian (1PN) approximation. There arises an integrability condition, that leads to the emergence of two types of general-relativistic corrections to a Newtonian rotation curve. The well known geometric dragging of frames accelerates rotation but the hitherto unknown dynamic term, that reflects the disk structure, deccelerates rotation. The net result can diminish the Newtonian angular velocity of rotation in a central disk zone but the geometric dragging of frames dominates in the disk boundary zone. Both effects are nonlinear in nature and they disappear in the limit of test fluids. Dust disks can be only geometrically dragged while uniformly rotating gaseous disk are untouched at the 1PN order. General-relativistic contributions can strongly affect rotation periods in Keplerian motion for compact systems.