On the black hole limit of rotating discs and rings

Details On the black hole limit of rotating discs and rings On the black hole limit of rotating discs and rings

2010-07-20

arxiv.org/abs/1007.3360v1

Gen.Rel.Grav.43:1469-1486,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 4 figures; Dedicated to Gernot Neugebauer on the occasion of his 70th birthday

Scientific paper

10.1007/s10714-010-1135-9

Solutions to Einstein's field equations describing rotating fluid bodies in equilibrium permit parametric (i.e. quasi-stationary) transitions to the extreme Kerr solution (outside the horizon). This has been shown analytically for discs of dust and numerically for ring solutions with various equations of state. From the exterior point of view, this transition can be interpreted as a (quasi) black hole limit. All gravitational multipole moments assume precisely the values of an extremal Kerr black hole in the limit. In the present paper, the way in which the black hole limit is approached is investigated in more detail by means of a parametric Taylor series expansion of the exact solution describing a rigidly rotating disc of dust. Combined with numerical calculations for ring solutions our results indicate an interesting universal behaviour of the multipole moments near the black hole limit.

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