Rotating systems, universal features in dragging and anti-dragging effects, and bounds onto angular momentum

Abstract

We consider stationary, axially symmetric toroids rotating around spinless black holes, assuming the general-relativistic Keplerian rotation law, in the first post-Newtonian approximation. Numerical investigation shows that the angular momentum accumulates almost exclusively within toroids. It appears that various types of dragging (anti-dragging) effects are positively correlated with the ratio $M_{\mathrm{D}}/m$ ($M_{\mathrm{D}}$ is the mass of a toroid and $m$ is the mass of the black hole) - moreover, their maxima are proportional to $M_{\mathrm{D}}/m$. The horizontal sizes of investigated toroids range from c. 50 to c. 450 of Schwarzschild radii $R_{\mathrm{S}}$ of the central black hole; their mass $M_{\mathrm{D}}\in (10^{-4}m,40m)$ and the radial size of the system is c. 500 $R_{\mathrm{S}}$. We found that the relative strength of various dragging (anti-dragging) effects does not change with the mass ratio, but it depends on the size of toroids. Several isoperimetric inequalities involving angular momentum are shown to hold true.

Revised and corrected, 14 pages, to appear in Physical Review D

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• Relativistic effects cannot explain galactic dynamics
• Two mass conjectures on axially symmetric black hole--disk systems
• General-relativistic rotation laws in fluid tori around spinning black holes
• On extensions of the Penrose inequality with angular momentum