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

Abstract

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 black hole, one obtains in the first post-Newtonian (1PN) approximation the hitherto known results, that can be interpreted as the geometric dragging and material antidragging. We find new 1PN effects, that are due to spins of black holes.

Stationary massive disks around black holes: Realistic equation of state and bifurcation

“…The second is formally more complex, but it gives the right and exact answer in the case of a masless disk around a Kerr black hole [16] (in such a case δ = −1/3 and κ = 3) and also gives monomial Newtonian limits for the angular velocity. We show, that the family of rotation laws of [1] is a subcase of that considered in [15].…”

“…We choose two families of rotation laws, that of [1] and of [15]. They are natural, for different reasons.…”

“…It is known that the rotation law of [1] excludes compact Keplerian solutions with light disks. In contrast to that, a Keplerian law of [15] does allow for compact solutions with light disks for a range of the specific entropy. These tori can gain a mass of the order of 0.06M if the specific entropy s is relatively low.…”

“…A rotation law describing disks in motion around black holes has been obtained in [14]. In what follows we focus on its generalization-a new family of rotation laws that was derived recently [15]. This family includes the Keplerian rotation, by which we mean a special case of the rotation law derived in [16]see Eq.…”

“…We get a satisfactory agreement with results of [1] in all analysed cases. We compare also disk solutions that satisfy the same boundary data, but different rotation laws-those of [1] and of [15]. We describe examples of bifurcation in Sec.…”