Proof of the (local) angular momemtum-mass inequality for axisymmetric black holes

We prove that for any vacuum, maximal, asymptotically flat, axisymmetric initial data for Einstein equations close to extreme Kerr data, the inequality

\sqrt{J} \leq m

is satisfied, where

m

and

J

are the total mass and angular momentum of the data. The proof consists in showing that extreme Kerr is a local minimum of the mass.

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References(7)

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- Commun.Pure Appl.Math. 39 661

Variational methods and positive energy in general relativity

D.R. Brill
(
- Yale U.
)
,
Stanley Deser
(
- Brandeis U.
)

- Annals Phys. 50 (1968) 548-570
•
DOI:
- 10.1016/0003-4916(68)90131-0

Axisymmetric Black Hole Has Only Two Degrees of Freedom

B. Carter
(
- Cambridge U., Inst. of Astron.
)

- Phys.Rev.Lett. 26 (1971) 331-333
•
DOI:
- 10.1103/PhysRevLett.26.331

- Commun.Math.Phys. 51 283

A Variational principle for stationary, axisymmetric solutions of Einstein's equations

Sergio Dain
(
- Potsdam, Max Planck Inst.
)

- Class.Quant.Grav. 23 (2006) 6857-6872
•
e-Print:
- gr-qc/0508061
•
DOI:
- 10.1088/0264-9381/23/23/016

New conformally flat initial data for spinning black holes

- Phys.Rev.D 65 (2002) 104038
•
e-Print:
- gr-qc/0201062
•
DOI:
- 10.1103/PhysRevD.65.104038

- J.Math.Phys. 23 109