Proof of the (local) angular momemtum-mass inequality for axisymmetric black holes
نویسنده
چکیده
We prove that for any vacuum, maximal, asymptotically flat, axisymmetric initial data for Einstein equations close to extreme Kerr data, the inequality √ J ≤ 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.
منابع مشابه
Proof of the angular momentum-mass inequality for axisymmetric black holes
We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent nonstationary, axially symmetric, black holes. As a consequence, we obtain that any data in this class satisfy the inequality √ J ≤ m, where ...
متن کاملThe Positive Mass Theorem for Multiple Rotating Charged Black Holes
In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes. We also weaken the hypotheses used in the proof of this result for single bl...
متن کاملProof of the Mass-angular Momentum Inequality for Bi-axisymmetric Black Holes with Spherical Topology
We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the mass-angular momentum inequality in this setting for 5-dimensional spacetimes. That is, all data in this class...
متن کاملProof of the (local) angular momentum–mass inequality for axisymmetric black holes
where m is the mass of the data and J is the angular momentum in the asymptotic region. Moreover, the equality in (1) should imply that the data are the slice of the extreme Kerr black hole. For a more detailed discussion of the motivations and relevance of (1) and related inequalities see [5–8, 10]. In [6], the proof of (1), for maximal data, was reduced to a variational problem. In this paper...
متن کاملArea-angular-momentum inequality for axisymmetric black holes.
We prove the local inequality A≥8π|J|, where A and J are the area and angular momentum of any axially symmetric closed stable minimal surface in an axially symmetric maximal initial data. From this theorem it is proved that the inequality is satisfied for any surface on complete asymptotically flat maximal axisymmetric data. In particular it holds for marginal or event horizons of black holes. ...
متن کامل