154 research outputs found
Angular momentum-mass inequality for axisymmetric black holes
In these notes we describe recent results concerning the inequality 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 Í“Phys. Z. Sovjetunion 10, 34 Í‘1936Í’; 1, 88 Í‘1932Í’; 2, 46 Í‘1932Í’Í” and Schwartz et al. Í“J. Chem. Phys. 20, 1591 Í‘1952Í’Í” 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
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