4,100 research outputs found
Applying black hole perturbation theory to numerically generated spacetimes
Nonspherical perturbation theory has been necessary to understand the meaning
of radiation in spacetimes generated through fully nonlinear numerical
relativity. Recently, perturbation techniques have been found to be successful
for the time evolution of initial data found by nonlinear methods. Anticipating
that such an approach will prove useful in a variety of problems, we give here
both the practical steps, and a discussion of the underlying theory, for taking
numerically generated data on an initial hypersurface as initial value data and
extracting data that can be considered to be nonspherical perturbations.Comment: 14 pages, revtex3.0, 5 figure
Cauchy-perturbative matching and outer boundary conditions: computational studies
We present results from a new technique which allows extraction of
gravitational radiation information from a generic three-dimensional numerical
relativity code and provides stable outer boundary conditions. In our approach
we match the solution of a Cauchy evolution of the nonlinear Einstein field
equations to a set of one-dimensional linear equations obtained through
perturbation techniques over a curved background. We discuss the validity of
this approach in the case of linear and mildly nonlinear gravitational waves
and show how a numerical module developed for this purpose is able to provide
an accurate and numerically convergent description of the gravitational wave
propagation and a stable numerical evolution.Comment: 20 pages, RevTe
Calculation of gravitational wave forms from black hole collisions and disk collapse: Applying perturbation theory to numerical spacetimes
Many simulations of gravitational collapse to black holes become inaccurate
before the total emitted gravitational radiation can be determined. The main
difficulty is that a significant component of the radiation is still in the
near-zone, strong field region at the time the simulation breaks down. We show
how to calculate the emitted waveform by matching the numerical simulation to a
perturbation solution when the final state of the system approaches a
Schwarzschild black hole. We apply the technique to two scenarios: the head-on
collision of two black holes, and the collapse of a disk to a black hole. This
is the first reasonably accurate calculation of the radiation generated from
colliding black holes that form from matter collapse.Comment: 8 pages (RevTex 3.0 with 7 uuencoded figures
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
A case study exploration of the therapeutic phenomena of projective identification, transference and countertransference : a brief therapy with a patient with psychotic anxiety
Bibliography: leaves 68-74.This dissertation reviews the concepts of projective identification, transference and countertransference from an Object Relations theoretical perspective. The developmental mother-infant relationship is explored as a model for understanding the therapist-patient interaction in both its normal and pathological forms . Projective identification is used to illuminate the workings of transference and countertransference. W.R. Bion's conception of the mother-therapist as 'Container' and infant-patient as 'Contained' is presented as pivotal to understanding that interaction. Failures in projective identification - and therefore in symbolic functioning - are explored, with particular focus given to psychotic and psychosomatic manifestations in patients. The relevance of transference and countertransference phenomena to brief psychotherapy is also considered. These concepts are then applied to a specific therapeutic case. The patient was seen as an in-and outpatient over a 5 month period 1-3 times per week. The patient's history and a brief formulation are presented, followed by a discussion of how the above-mentioned theoretical issues manifested in the therapy. The patient operated on the border between psychosis and neurosis and communicated in primitive pre-verbal and powerful symbolic ways. Case illustrations focus on the interplay between her psyche and soma, the impact of the hospital setting as well as particular transference and countertransference difficulties incurred
Weak-localization and rectification current in non-diffusive quantum wires
We show that electron transport in disordered quantum wires can be described
by a modified Cooperon equation, which coincides in form with the Dirac
equation for the massive fermions in a 1+1 dimensional system. In this new
formalism, we calculate the DC electric current induced by electromagnetic
fields in quasi-one-dimensional rings. This current changes sign, from
diamagnetic to paramagnetic, depending on the amplitude and frequency of the
time-dependent external electromagnetic field.Comment: changed title, added more detail, to appear in J. Phys.: Condens.
Matte
Waveform propagation in black hole spacetimes: evaluating the quality of numerical solutions
We compute the propagation and scattering of linear gravitational waves off a
Schwarzschild black hole using a numerical code which solves a generalization
of the Zerilli equation to a three dimensional cartesian coordinate system.
Since the solution to this problem is well understood it represents a very good
testbed for evaluating our ability to perform three dimensional computations of
gravitational waves in spacetimes in which a black hole event horizon is
present.Comment: 13 pages, RevTeX, to appear in Phys. Rev.
The collision of boosted black holes
We study the radiation from a collision of black holes with equal and
opposite linear momenta. Results are presented from a full numerical relativity
treatment and are compared with the results from a ``close-slow''
approximation. The agreement is remarkable, and suggests several insights about
the generation of gravitational radiation in black hole collisions.Comment: 8 pages, RevTeX, 3 figures included with eps
The Evolution of Distorted Rotating Black Holes II: Dynamics and Analysis
We have developed a numerical code to study the evolution of distorted,
rotating black holes. This code is used to evolve a new family of black hole
initial data sets corresponding to distorted ``Kerr'' holes with a wide range
of rotation parameters, and distorted Schwarzschild black holes with odd-parity
radiation. Rotating black holes with rotation parameters as high as
are evolved and analyzed in this paper. The evolutions are generally carried
out to about , where is the ADM mass. We have extracted both the
even- and odd-parity gravitational waveforms, and find the quasinormal modes of
the holes to be excited in all cases. We also track the apparent horizons of
the black holes, and find them to be a useful tool for interpreting the
numerical results. We are able to compute the masses of the black holes from
the measurements of their apparent horizons, as well as the total energy
radiated and find their sum to be in excellent agreement with the ADM mass.Comment: 26 pages, LaTeX with RevTeX 3.0 macros. 27 uuencoded gz-compressed
postscript figures. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/
Submitted to Physical Review
Gravitational wave extraction and outer boundary conditions by perturbative matching
We present a method for extracting gravitational radiation from a
three-dimensional numerical relativity simulation and, using the extracted
data, to provide outer boundary conditions. The method treats dynamical
gravitational variables as nonspherical perturbations of Schwarzschild
geometry. We discuss a code which implements this method and present results of
tests which have been performed with a three dimensional numerical relativity
code
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