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.
Highlights
Symmetric and stationary Newtonian hydrodynamic configurations are known for a long time to be characterized by a rich variety of rotation curves
Quite recently two of us have found general-relativistic rotation curves j = j(Ω) [5] that in the nonrelativistic limit exactly coincide with all monomial rotation laws Ω0 = w/r2/(1−δ), with the exception of the constant linear velocity case (−∞ ≤ δ ≤ 0, δ = −1, w = const)
The main purpose of this paper is to show that the problematic case of constant linear velocity is included in the proposed family of general-relativistic rotations
Summary
Symmetric and stationary Newtonian hydrodynamic configurations are known for a long time to be characterized by a rich variety of rotation curves. In general relativity had been known only two families of rotation laws—one with j being a linear function of the angular velocity Ω [1,2,3] and a more recent nonlinear angular velocity proposal [4]. Their Newtonian limits recover only a small fraction of the set of Newtonian rotation curves. The main purpose of this paper is to show that the problematic case of constant linear velocity is included in the proposed family of general-relativistic rotations
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