Virial tests for post-Newtonian stationary black-hole-disk systems

TL;DR

This paper develops post-Newtonian models for stationary black-hole-disk systems, revealing significant relativistic effects on disk dynamics that depend on both radial and vertical positions.

Contribution

It introduces a post-Newtonian scheme for black-hole-disk systems, extending previous Newtonian models and highlighting relativistic corrections at the 1PN level.

Findings

1PN correction to angular velocity can reach 10% of Newtonian value

Relativistic effects depend on both radial and vertical positions

Post-Newtonian scheme improves modeling accuracy for black-hole-disk systems

Abstract

We investigated hydrodynamical post-Newtonian models of selfgravitating stationary black-hole-disk systems. The post-Newtonian scheme presented here and also in our recent paper is a continuation of previous, purely Newtonian studies of selfgravitating hydrodynamical disks rotating according to the Keplerian rotation law. The post-Newtonian relativistic corrections are significant even at the 1PN level. The 1PN correction to the angular velocity can be of the order of 10% of its Newtonian value. It can be expressed as a combination of geometric and hydrodynamical terms. Moreover, in contrast to the Newtonian Poincare-Wavre theorem, it depends both on the distance from the rotation axis and the distance from the equatorial plane.