Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-07-30
Phys.Rev.D82:104010,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages. Changes in presentation and typos corrections
Scientific paper
10.1103/PhysRevD.82.104010
We present a formula that relates the variations of the area of extreme throat initial data with the variation of an appropriate defined mass functional. From this expression we deduce that the first variation, with fixed angular momentum, of the area is zero and the second variation is positive definite evaluated at the extreme Kerr throat initial data. This indicates that the area of the extreme Kerr throat initial data is a minimum among this class of data. And hence the area of generic throat initial data is bounded from below by the angular momentum. Also, this result strongly suggests that the inequality between area and angular momentum holds for generic asymptotically flat axially symmetric black holes. As an application, we prove this inequality in the non trivial family of spinning Bowen-York initial data.
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