General-relativistic Rotation Laws in Rotating Fluid Bodies: Constant Linear Velocity

Abstract

New rotation laws have been recently found for general-relativistic self-gravitating stationary fluids. It was not clear whether they apply to systems rotating with a constant linear velocity. In this paper we fill this gap. The answer is positive. That means, in particular, that these systems should exhibit the recently discovered general-relativistic weak-field effects within rotating tori: the dynamic anti-dragging and the deviation from the Keplerian motion induced by the fluid selfgravity.

Self-gravitating axially symmetric disks in general-relativistic rotation

“…We recovered many of solutions found in [9]. Our results agree well in the post-Newtonian regime with the earlier post-Newtonian analysis (see [7,22,25]), but the related material will be published elsewhere.…”

“…On the other hand, for our model with the rotation law (22), and with the same spin parameter of the central black hole, a = 0.9, the situation becomes confusing. We get R con 5 ± 1 at best, with a large variation for some metric functions (see Fig.…”

“…Numerical results, reported below, suggest that in fact the general-relativistic Keplerian rotation is best described by (22). Clearly the parameter w is not free-its value constitutes a part of a solution.…”

“…For example, if one of the metric function is well-approximated by a quadratic polynomial, the 2nd order scheme could yield almost exact solution of the discretized system instantly. In the lower part the black hole has a = 0.9 and the torus rotates according to (22).…”

Two mass conjectures on axially symmetric black hole-disk systems

“…The general-relativistic rotation has been investigated since early 1970's -primarily a rigid rotation [19,20] and its modifications [21][22][23]. New general-relativistic differential rotation laws j = j(Ω), where j denotes the specific angular momentum, have recently been found for stationary systems consisting of self-gravitating toroids around spinless [24,25] and spinning black holes [3,4]. They describe, in particular, the motion of a massless disks of dust, with Ω = √ GM ADM /r 3/2 C in the case of the Schwarzschild geometry.…”