On the multipole moments of a rigidly rotating fluid body

Filter, Robert; Kleinwächter, Andreas

doi:10.1002/andp.200910337

Cited by 2 publications

(2 citation statements)

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“…We also mention that, according to our experience, the exterior spacetime of a uniformly rotating fluid body is never described by the Kerr metric-except for the black hole limit e V 0 → 0 . As long as e V 0 = 0, all "higher" multipole moments (beyond M and J ) always seem to be greater than those of the corresponding Kerr spacetime [29].…”

Section: Discussionmentioning

confidence: 95%

On the black hole limit of rotating discs and rings

2010

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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.Comment: 18 pages, 4 figures; Dedicated to Gernot Neugebauer on the occasion of his 70th birthda

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Section: Discussionmentioning

confidence: 95%

On the black hole limit of rotating discs and rings

2010

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“…12 An interesting general feature of the exterior field of uniformly rotating perfect fluid bodies seems to be that all gravitational multipole moments beyond M and J, in particular the quadrupole moment, are greater than or equal to the corresponding moments of the Kerr metric with the same mass and angular momentum. 13 The equality holds (presumably only) in the case of a "black hole limit" where all multipole moments become precisely those of the extreme Kerr metric. 14 This will be discussed in more detail in the next section.…”

Section: Numerical Treatment Of the General Casementioning

confidence: 99%