General-relativistic rotation laws in rotating fluid bodies

  title={General-relativistic rotation laws in rotating fluid bodies},
  author={Patryk Mach and Edward J Malec},
  journal={Physical Review D},
We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to re-derive, in the first post-Newtonian approximation, the well known geometric dragging of frames. We derive two other general-relativistic weak-field effects within rotating tori: the recently discovered dynamic anti-dragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids selfgravity. One can use… 

Figures from this paper

General-relativistic rotation laws in fluid tori around spinning black holes

We obtain rotation laws for axially symmetric, selfgravitating and stationary fluids around spinning black holes. They reduce --- in the Newtonian limit --- to monomial rotation curves. For spinless

General-relativistic rotation: Self-gravitating fluid tori in motion around black holes

We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was

Self-gravitating axially symmetric disks in general-relativistic rotation

We integrate numerically axially symmetric stationary Einstein equations describing self-gravitating disks around spinless black holes. The numerical scheme is based on a method developed by Shibata,

Rotating stars in relativity

The latest theoretical understanding of rotating stars in relativity is reviewed and several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, and on analytic solutions for the exterior spacetime.

Toroidal magnetic fields in self-gravitating disks around black holes

We investigate stationary models of magnetized, self-gravitating disks around black holes. The disks are assumed to rotate according to a recently introduced Keplerian rotation law. We consider

Accretion processes for general spherically symmetric compact objects

We investigate the accretion process for different spherically symmetric space-time geometries for a static fluid. We analyze this procedure using the most general black hole metric ansatz. After

Two mass conjectures on axially symmetric black hole-disk systems

We analyze stationary self-gravitating disks around spinning black holes that satisfy the recently found general-relativistic Keplerian rotation law. There is a numerical evidence that the angular

Equilibrium sequences of differentially rotating stars with post-merger-like rotational profiles

We present equilibrium sequences of rotating relativistic stars, constructed with a new rotation law that was proposed by Uryu et al. (2017). We choose rotational parameters motivated by simulations

Rotating systems, universal features in dragging and antidragging effects, and bounds of angular momentum

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

Spherical accretion by normal and phantom Einstein–Maxwell–dilaton black holes

We investigate the spherical accretion process for general static spherically symmetric fluids. We analyze this process by using the general metric ansatz for spherically symmetric black holes. We




  • Rev. 62, art. id. 021501
  • 2000

to appear in Phys

  • Rev. D, arXiv:1410.8527
  • 2014


  • J. 200, L103
  • 1969

ASP Conference Series 395

  • 87
  • 2008

Acta Phys

  • Pol. B44, 107
  • 2013


  • J. 195, L65
  • 1975


  • Lett. 20, 504
  • 1966

Stellar Rotation (Cambridge

  • 2007


  • J. 162, 71
  • 1970


  • J. 727, art. id. 95
  • 2011