相关论文: Angular momentum-mass inequality for axisymmetric …
In these notes we describe recent results concerning the inequality $m\geq \sqrt{|J|}$ for axially symmetric 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…
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…
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…
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…
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several…
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 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…
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…
A Kerr black hole with mass $M$ and angular momentum $J$ satisfies the extremality inequality $|J| \le M^2$. In the presence of matter and/or gravitational radiation, this bound needs to be reformulated in terms of local measurements of the…
We give a comprehensive discussion, including a detailed proof, of the area-angular momentum-charge inequality for axisymmetric black holes. We analyze the inequality from several viewpoints, in particular including aspects with a…
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 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…
It is well known that the three parameters that characterize the Kerr black hole (mass, angular momentum and horizon area) satisfy several important inequalities. Remarkably, some of these inequalities remain valid also for dynamical black…
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.
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 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 fixed a two-surface. These initial conditions have been…
We prove the Penrose inequality with angular momentum for asymptotically flat, axisymmetric vacuum initial data sets containing a stable marginally outer trapped surface. This inequality provides a lower bound for the ADM mass in terms of…
We establish inequalities relating the size of a material body to its mass, angular momentum, and charge, within the context of axisymmetric initial data sets for the Einstein equations. These inequalities hold in general without the…
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…