In this essay I first discuss the physical relevance of the inequality for axially symmetric
(nonstationary) black holes, where m is the mass and J the angular momentum of the space …

We present numerical evidences for the validity of the inequality between the total mass and
the total angular momentum for multiple axially symmetric (nonstationary) black holes. We …

We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr
black hole, there exists a positive definite and conserved energy. This provides a basic …

We prove that an 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 …

This a brief introduction to the sequence of works\cite {KS: Kerr},\cite {GKS-2022},\cite {KS-
GCM1},\cite {KS-GCM2} and\cite {Shen} which establish the nonlinear stability of Kerr black …

Kerr black holes (BHs) have their angular momentum, J, bounded by their mass, M: J c≤
GM 2. There are, however, known BH solutions violating this Kerr bound. We propose a very …

This a brief introduction to the sequence of works [KS: Kerr],[GKS-2022],[KS: GCM1],[KS:
GCM2] and [Shen] which establish the nonlinear stability of Kerr black holes with small …

A Kerr black hole with mass M and angular momentum J satisfies the extremality inequality|
J|≤ M 2. In the presence of matter and/or gravitational radiation, this bound needs to be …

Fast Track Communications Page 1 Classical and Quantum Gravity FAST TRACK
COMMUNICATION A universal inequality between the angular momentum and horizon area for …

We prove an inequality between horizon area and angular momentum for a class of axially
symmetric black holes. This class includes initial conditions with an isometry which leaves …