On the Stability of Circular Orbits of Particles Moving around Black Holes Surrounded by Axially Symmetric Structures

TL;DR

This paper investigates the stability of circular particle orbits around black holes with axially symmetric structures, using the Rayleigh criterion, and compares relativistic and Newtonian cases, highlighting the tendency for ring formation in relativistic dynamics.

Contribution

It introduces a detailed analysis of orbit stability around black holes with various axially symmetric structures, incorporating quadrupole moments and comparing relativistic and Newtonian results.

Findings

Relativistic dynamics favor the formation of rings.

Stability of disks is linked to test particle stability under counter-rotation.

Comparison shows differences between Newtonian and relativistic stability criteria.

Abstract

The Rayleigh criterion is used to study the stability of circular orbits of particles moving around static black holes surrounded by different axially symmetric structures with reflection symmetry, like disks, rings and halos. We consider three models of disks one of infinite extension and two finite, and one model of rings. The halos are represented by external quadrupole moments (either oblate or prolate). Internal quadrupole perturbation (oblate and prolate) are also considered. For this class of disks the counter-rotation hypothesis implies that the stability of the disks is equivalent to the stability of test particles. The stability of Newtonian systems is also considered and compared with the equivalent relativistic situation. We find that the general relativistic dynamics favors the formation of rings.