Angular momentum-mass inequality for axisymmetric black holes

In these notes we describe recent results concerning the inequality $m\geq \sqrt{|J|}$ for axially symmetric black holes.Comment: 7 pages, 1 figur

A Dain Inequality with charge

We prove an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space

Initial data for fluid bodies in general relativity

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary. PACS: 04.20.Ex, 04.40.Nr, 02.30.JrComment: 38 pages, LaTeX 2e, no figures. Accepted for publication in Phys. Rev.

Black Hole Interaction Energy

The interaction energy between two black holes at large separation distance is calculated. The first term in the expansion corresponds to the Newtonian interaction between the masses. The second term corresponds to the spin-spin interaction. The calculation is based on the interaction energy defined on the two black holes initial data. No test particle approximation is used. The relation between this formula and cosmic censorship is discussed.Comment: 18 pages, 2 figures, LaTeX2

Existence and uniqueness of Bowen-York Trumpets

We prove the existence of initial data sets which possess an asymptotically flat and an asymptotically cylindrical end. Such geometries are known as trumpets in the community of numerical relativists.Comment: This corresponds to the published version in Class. Quantum Grav. 28 (2011) 24500

A new geometric invariant on initial data for Einstein equations

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the non-time symmetric cas

Initial data for a head on collision of two Kerr-like black holes with close limit

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. This family of initial data has the following properties: (i) When the mass parameter of one of them is zero or when the distance between them goes to infinity, it reduces exactly to the Kerr initial data. (ii) When the distance between them is zero, we obtain exactly a Kerr initial data with mass and angular momentum equal to the sum of the mass and angular momentum parameters of each of them. The initial data depends smoothly on the distance, the mass and the angular momentum parameters.Comment: 15 pages, no figures, Latex2

Acoustic Attenuation in Three-Component Gas Mixtures

Vibrational relaxation accounts for absorption and dispersion of acoustic waves in gases that can be significantly greater than the classical absorption mechanisms related to shear viscosity and heat conduction. This vibrational relaxation results from retarded energy exchange between translational and intramolecular vibrational degrees of freedom. Theoretical calculation of the vibrational relaxation time of gases based on the theory of Landau and Teller ͓Phys. Z. Sovjetunion 10, 34 ͑1936͒; 1, 88 ͑1932͒; 2, 46 ͑1932͔͒ and Schwartz et al. ͓J. Chem. Phys. 20, 1591 ͑1952͔͒ has been applied at room temperature to ternary mixtures of polyatomic gases containing nitrogen, water vapor, and methane. Due to vibrational-translational and vibrational-vibrational coupling between all three components in ternary mixtures, multiple relaxation processes produce effective relaxation frequencies affecting the attenuation of sound. The dependence of effective relaxation frequencies and the attenuation on mole fractions of the constituents was investigated. The acoustic attenuation in a mixture that is primarily nitrogen is strongly dependent on the concentrations of methane and water vapor that are present. However, the attenuation in a mixture that is primarily methane is only weakly dependent on the concentrations of nitrogen and water vapor. The theory developed in this paper is applicable to other multicomponent mixtures

Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes

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 stationary axially symmetric Einstein equations. As a by product our method, we also give numerical evidences that there are no regular solutions of Einstein equations that describe two extreme, axially symmetric black holes in equilibrium.Comment: 16 pages, 10 figure

Axisymmetric evolution of Einstein equations and mass conservation

For axisymmetric evolution of isolated systems, we prove that there exists a gauge such that the total mass can be written as a positive definite integral on the spacelike hypersurfaces of the foliation and the integral is constant along the evolution. The conserved mass integral controls the square of the extrinsic curvature and the square of first derivatives of the intrinsic metric. We also discuss applications of this result for the global existence problem in axial symmetry.Comment: A mistake in the proof of Lemma 5.1 is corrected. This version includes the Corrigendum that appears in Class. Quantum Grav. 26 (2009) 12980