561 research outputs found
Linear perturbations for the vacuum axisymmetric Einstein equations
In axial symmetry, there is a gauge for Einstein equations such that the
total mass of the spacetime can be written as a conserved, positive definite,
integral on the spacelike slices. This property is expected to play an
important role in the global evolution. In this gauge the equations reduce to a
coupled hyperbolic-elliptic system which is formally singular at the axis. Due
to the rather peculiar properties of the system, the local in time existence
has proved to resist analysis by standard methods. To analyze the principal
part of the equations, which may represent the main source of the difficulties,
we study linear perturbation around the flat Minkowski solution in this gauge.
In this article we solve this linearized system explicitly in terms of integral
transformations in a remarkable simple form. This representation is well suited
to obtain useful estimates to apply in the non-linear case.Comment: 13 pages. We suppressed the statements about decay at infinity. The
proofs of these statements were incomplete. The complete proofs will require
extensive technical analysis. We will studied this in a subsequent work. We
also have rewritten the introduction and slighted changed the titl
The Yamabe invariant for axially symmetric two Kerr black holes initial data
An explicit 3-dimensional Riemannian metric is constructed which can be
interpreted as the (conformal) sum of two Kerr black holes with aligned angular
momentum. When the separation distance between them is large we prove that this
metric has positive Ricci scalar and hence positive Yamabe invariant. This
metric can be used to construct axially symmetric initial data for two Kerr
black holes with large angular momentum.Comment: 14 pages, 2 figure
Generalized Korn's inequality and conformal Killing vectors
Korn's inequality plays an important role in linear elasticity theory. This
inequality bounds the norm of the derivatives of the displacement vector by the
norm of the linearized strain tensor. The kernel of the linearized strain
tensor are the infinitesimal rigid-body translations and rotations (Killing
vectors). We generalize this inequality by replacing the linearized strain
tensor by its trace free part. That is, we obtain a stronger inequality in
which the kernel of the relevant operator are the conformal Killing vectors.
The new inequality has applications in General Relativity.Comment: 8 page
Black hole Area-Angular momentum inequality in non-vacuum spacetimes
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 non-necessarily axisymmetric black hole spacetimes, with non-negative
cosmological constant and whose matter content satisfies the dominant energy
condition.Comment: 5 pages, no figures, updated to match published versio
Initial data for stationary space-times near space-like infinity
We study Cauchy initial data for asymptotically flat, stationary vacuum
space-times near space-like infinity. The fall-off behavior of the intrinsic
metric and the extrinsic curvature is characterized. We prove that they have an
analytic expansion in powers of a radial coordinate. The coefficients of the
expansion are analytic functions of the angles. This result allow us to fill a
gap in the proof found in the literature of the statement that all
asymptotically flat, vacuum stationary space-times admit an analytic
compactification at null infinity. Stationary initial data are physical
important and highly non-trivial examples of a large class of data with similar
regularity properties at space-like infinity, namely, initial data for which
the metric and the extrinsic curvature have asymptotic expansion in terms of
powers of a radial coordinate. We isolate the property of the stationary data
which is responsible for this kind of expansion.Comment: LaTeX 2e, no figures, 12 page
Close limit evolution of Kerr-Schild type initial data for binary black holes
We evolve the binary black hole initial data family proposed by Bishop {\em
et al.} in the limit in which the black holes are close to each other. We
present an exact solution of the linearized initial value problem based on
their proposal and make use of a recently introduced generalized formalism for
studying perturbations of Schwarzschild black holes in arbitrary coordinates to
perform the evolution. We clarify the meaning of the free parameters of the
initial data family through the results for the radiated energy and waveforms
from the black hole collision.Comment: 8 pages, RevTex, four eps figure
Navlisp Reference Manual
The Naval Postgraduate School's Computer Laboratory has developed a dialect of LISP, called Navlisp, to run under PWB/UNIX on a PDP11/50. This manual is not a tutorial to LISP. It is intended for those who know the basics of the LISP programming language and wish to use the Navlisp dialect.Chief Of Naval Researc
Implement modified version of Nestle oil test on flexible packaging film to evaluate migration of essential oils on films coated with layered nanoclay platelets.
Project followed a previous research method established by Nestle Purina for test of grease migration in Pet Food packaging using chicken fat and oleic acid. This procedure was modified and replaced with Essential oils commonly found in spices and seasoning blends. The objective was to observe the barrier effectiveness of an emerging coating technology (Nanoseal) using less than one micron thick layer of exfoliated clay platelets coated on thin packaging film commonly used in food packaging. Use the Nestle method to track Migration of Essential oils detectable under natural and UV light exposed to chromatography plates under ambient and elevated temperature with direct pressure applied to the test film surface. High temperatures in the procedure lead to evaporation of the oil in early test phases. NanoGold trace element later added to the oil as another tool to help track permeation in the film and clay platelet layer. The gold trace element as a marker proved inconclusive
Conformally flat black hole initial data, with one cylindrical end
We give a complete analytical proof of existence and uniqueness of
extreme-like black hole initial data for Einstein equations, which possess a
cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and
extreme Bowen-York's initial data. This extends and refines a previous result
\cite{dain-gabach09} to a general case of conformally flat, maximal initial
data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published
version in Class. Quantum Grav. (2010). Results unchange
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
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