Related papers: Mass-Angular Momentum Inequality For Black Ring Sp…
We show that the area-angular momentum-charge inequality (A/(4\pi))^2 \geq (2J)^2 + (Q_E^2 + Q_M^2)^2 holds for apparent horizons of electrically and magnetically charged rotating black holes in generic dynamical and non-vacuum spacetimes.…
In this essay I first discuss the physical relevance of the inequality $m\geq \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this…
For a stable marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant $\Lambda > 0$ and with matter satisfying the dominant energy condition, we prove that the area $A$ and the angular momentum…
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…
The inequality $\sqrt{J}\leq m$ is proved for vacuum, asymptotically flat, maximal and axisymmetric data close to extreme Kerr data. The physical significance of this inequality and its relation to the standard picture of the gravitational…
In these notes we describe recent results concerning the inequality $m\geq \sqrt{|J|}$ for axially symmetric black holes.
We show that the area-angular momentum inequality A\geq 8\pi|J| holds for axially symmetric closed outermost stably marginally trapped surfaces. These are horizon sections (in particular, apparent horizons) contained in otherwise generic…
We consider $n$-dimensional spacetimes which are axisymmetric--but not necessarily stationary (!)--in the sense of having isometry group $U(1)^{n-3}$, and which satisfy the Einstein equations with a non-negative cosmological constant. We…
We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality $8\pi|J|<A$ holds, where $J$ is the angular momentum and $A$ the horizon area of the black hole.
This is the second in a series of two papers to establish the conjectured mass-angular momentum inequality for multiple black holes, modulo the extreme black hole 'no hair theorem'. More precisely it is shown that either there is a…
We consider the quasi-black hole limit of a stationary body when its boundary approaches its own gravitational radius, i.e., its quasi-horizon. It is shown that there exists a perfect correspondence between the different mass contributions…
The general analysis of the relations between masses and angular momenta in the configurations composed of two balancing extremal Kerr particles is made on the basis of two exact solutions arising as extreme limits of the well-known…
A highly accurate computer program is used to study axially symmetric and stationary spacetimes containing a Black Hole surrounded by a ring of matter. It is shown that the matter ring affects the properties of the Black Hole drastically.…
We present numerical evidences for the validity of the inequality between the total mass and the total angular momentum for multiple axially symmetric (non-stationary) black holes. We use a parabolic heat flow to solve numerically the…
General regular black ring solution with two angular momenta is presented, found by the inverse scattering problem method. The mass, angular momenta and the event horizon volume are given explicitly as functions of the metric parameters.
In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. A new…
We prove the local inequality $A \geq 8\pi|J|$, 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…
We propose a new definition for the mass and angular momentum of neutral or electrically charged black holes in 2+1 gravity with two Killing vectors. These finite conserved quantities, associated with the SL(2,R) invariance of the reduced…
Geometrical inequalities show how certain parameters of a physical system set restrictions on other parameters. For instance, a black hole of given mass can not rotate too fast, or an ordinary object of given size can not have too much…
The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in…