4,325 research outputs found
Detector panels-micrometeoroid impact Patent
Development of large area micrometeoroid impact detector panel
Excision boundary conditions for black hole initial data
We define and extensively test a set of boundary conditions that can be
applied at black hole excision surfaces when the Hamiltonian and momentum
constraints of general relativity are solved within the conformal thin-sandwich
formalism. These boundary conditions have been designed to result in black
holes that are in quasiequilibrium and are completely general in the sense that
they can be applied with any conformal three-geometry and slicing condition.
Furthermore, we show that they retain precisely the freedom to specify an
arbitrary spin on each black hole. Interestingly, we have been unable to find a
boundary condition on the lapse that can be derived from a quasiequilibrium
condition. Rather, we find evidence that the lapse boundary condition is part
of the initial temporal gauge choice. To test these boundary conditions, we
have extensively explored the case of a single black hole and the case of a
binary system of equal-mass black holes, including the computation of
quasi-circular orbits and the determination of the inner-most stable circular
orbit. Our tests show that the boundary conditions work well.Comment: 23 pages, 23 figures, revtex4, corrected typos, added reference,
minor content changes including additional post-Newtonian comparison. Version
accepted by PR
The Angular Momentum Operator in the Dirac Equation
The Dirac equation in spherically symmetric fields is separated in two
different tetrad frames. One is the standard cartesian (fixed) frame and the
second one is the diagonal (rotating) frame. After separating variables in the
Dirac equation in spherical coordinates, and solving the corresponding
eingenvalues equations associated with the angular operators, we obtain that
the spinor solution in the rotating frame can be expressed in terms of Jacobi
polynomials, and it is related to the standard spherical harmonics, which are
the basis solution of the angular momentum in the Cartesian tetrad, by a
similarity transformation.Comment: 13 pages,CPT-94/P.3027,late
Collisions of boosted black holes: perturbation theory prediction of gravitational radiation
We consider general relativistic Cauchy data representing two nonspinning,
equal-mass black holes boosted toward each other. When the black holes are
close enough to each other and their momentum is sufficiently high, an
encompassing apparent horizon is present so the system can be viewed as a
single, perturbed black hole. We employ gauge-invariant perturbation theory,
and integrate the Zerilli equation to analyze these time-asymmetric data sets
and compute gravitational wave forms and emitted energies. When coupled with a
simple Newtonian analysis of the infall trajectory, we find striking agreement
between the perturbation calculation of emitted energies and the results of
fully general relativistic numerical simulations of time-symmetric initial
data.Comment: 5 pages (RevTex 3.0 with 3 uuencoded figures), CRSR-107
Can a combination of the conformal thin-sandwich and puncture methods yield binary black hole solutions in quasi-equilibrium?
We consider combining two important methods for constructing
quasi-equilibrium initial data for binary black holes: the conformal
thin-sandwich formalism and the puncture method. The former seeks to enforce
stationarity in the conformal three-metric and the latter attempts to avoid
internal boundaries, like minimal surfaces or apparent horizons. We show that
these two methods make partially conflicting requirements on the boundary
conditions that determine the time slices. In particular, it does not seem
possible to construct slices that are quasi-stationary and avoid physical
singularities and simultaneously are connected by an everywhere positive lapse
function, a condition which must obtain if internal boundaries are to be
avoided. Some relaxation of these conflicting requirements may yield a soluble
system, but some of the advantages that were sought in combining these
approaches will be lost.Comment: 8 pages, LaTeX2e, 2 postscript figure
The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach
We study the appearance of multiple solutions to certain decompositions of
Einstein's constraint equations. Pfeiffer and York recently reported the
existence of two branches of solutions for identical background data in the
extended conformal thin-sandwich decomposition. We show that the Hamiltonian
constraint alone, when expressed in a certain way, admits two branches of
solutions with properties very similar to those found by Pfeiffer and York. We
construct these two branches analytically for a constant-density star in
spherical symmetry, but argue that this behavior is more general. In the case
of the Hamiltonian constraint this non-uniqueness is well known to be related
to the sign of one particular term, and we argue that the extended conformal
thin-sandwich equations contain a similar term that causes the breakdown of
uniqueness.Comment: 9 pages, 1 figur
Computing the Complete Gravitational Wavetrain from Relativistic Binary Inspiral
We present a new method for generating the nonlinear gravitational wavetrain
from the late inspiral (pre-coalescence) phase of a binary neutron star system
by means of a numerical evolution calculation in full general relativity. In a
prototype calculation, we produce 214 wave cycles from corotating polytropes,
representing the final part of the inspiral phase prior to reaching the ISCO.
Our method is based on the inequality that the orbital decay timescale due to
gravitational radiation is much longer than an orbital period and the
approximation that gravitational radiation has little effect on the structure
of the stars. We employ quasi-equilibrium sequences of binaries in circular
orbit for the matter source in our field evolution code. We compute the
gravity-wave energy flux, and, from this, the inspiral rate, at a discrete set
of binary separations. From these data, we construct the gravitational waveform
as a continuous wavetrain. Finally, we discuss the limitations of our current
calculation, planned improvements, and potential applications of our method to
other inspiral scenarios.Comment: 4 pages, 4 figure
Current clinical practice: differential management of uveal melanoma in the era of molecular tumor analyses
Cauchy-perturbative matching and outer boundary conditions I: Methods and tests
We present a new method of extracting gravitational radiation from
three-dimensional numerical relativity codes and providing outer boundary
conditions. Our approach matches the solution of a Cauchy evolution of
Einstein's equations to a set of one-dimensional linear wave equations on a
curved background. We illustrate the mathematical properties of our approach
and discuss a numerical module we have constructed for this purpose. This
module implements the perturbative matching approach in connection with a
generic three-dimensional numerical relativity simulation. Tests of its
accuracy and second-order convergence are presented with analytic linear wave
data.Comment: 13 pages, 6 figures, RevTe
General Relativistic Models of Binary Neutron Stars in Quasiequilibrium
We perform fully relativistic calculations of binary neutron stars in
corotating, circular orbit. While Newtonian gravity allows for a strict
equilibrium, a relativistic binary system emits gravitational radiation,
causing the system to lose energy and slowly spiral inwards. However, since
inspiral occurs on a time scale much longer than the orbital period, we can
treat the binary to be in quasiequilibrium. In this approximation, we integrate
a subset of the Einstein equations coupled to the relativistic equation of
hydrostatic equilibrium to solve the initial value problem for binaries of
arbitrary separation. We adopt a polytropic equation of state to determine the
structure and maximum mass of neutron stars in close binaries for polytropic
indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate
turning points along energy equilibrium curves to identify the onset of orbital
instability. In particular, we locate the innermost stable circular orbit
(ISCO) and its angular velocity. We construct the first contact binary systems
in full general relativity. These arise whenever the equation of state is
sufficiently soft >= 1.5. A radial stability analysis reveals no tendency for
neutron stars in close binaries to collapse to black holes prior to merger.Comment: 14 pages, 8 figures, RevTe
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