149 research outputs found
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
Black hole collisions from Brill-Lindquist initial data: predictions of perturbation theory
The Misner initial value solution for two momentarily stationary black holes
has been the focus of much numerical study. We report here analytic results for
an astrophysically similar initial solution, that of Brill and Lindquist (BL).
Results are given from perturbation theory for initially close holes and are
compared with available numerical results. A comparison is made of the
radiation generated from the BL and the Misner initial values, and the physical
meaning is discussed.Comment: 11 pages, revtex3.0, 5 figure
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
Disk collapse in general relativity
The radial collapse of a homogeneous disk of collisionless particles can be solved analytically in Newtonian gravitation. To solve the problem in general relativity, however, requires the full machinery of numerical relativity. The collapse of a disk is the simplest problem that exhibits the two most significant and challenging features of strong-field gravitation: black hole formation and gravitational wave generation. We carry out dynamical calculations of several different relativistic disk systems. We explore the growth of ring instabilities in equilibrium disks, and how they are suppressed by sufficient velocity dispersion. We calculate waveforms from oscillating disks, and from disks that undergo gravitational collapse to black holes. Studies of disk collapse to black holes should also be useful for developing new techniques for numerical relativity, such as apparent horizon boundary conditions for black hole spacetimes
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 Electronic and Superconducting Properties of Oxygen-Ordered MgB2 compounds of the form Mg2B3Ox
Possible candidates for the Mg2B3Ox nanostructures observed in bulk of
polycrystalline MgB2 (Ref.1) have been studied using a combination of
Z-contrast imaging, electron energy loss spectroscopy (EELS) and
first-principles calculations. The electronic structures, phonon modes, and
electron phonon coupling parameters are calculated for two oxygen-ordered MgB2
compounds of composition Mg2B3O and Mg2B3O2, and compared with those of MgB2.
We find that the density of states for both Mg2B3Ox structures show very good
agreement with EELS, indicating that they are excellent candidates to explain
the observed coherent oxygen precipitates. Incorporation of oxygen reduces the
transition temperature and gives calculated TC values of 18.3 K and 1.6 K for
Mg2B3O and Mg2B3O2, respectively.Comment: Submitted to PR
Solving Einstein's equations for rotating spacetimes: Evolution of relativistic star clusters
A numerical relativity code designed to evolve rotating axisymmetric spacetimes is constructed. Both polarization states of gravitational radiation can be tracked. The source of the gravitational field is chosen to be a configuration of collisionless particles. The code is used to evaluate the stability of polytropic and toroidal star clusters. The formation of Kerr black holes by the collapse of unstable clusters is demonstrated. Unstable clusters with J/(M^2) 1 collapse to new equilibrium configurations
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
Vacuum initial data, singularities, and cosmic censorship
The formation of a naked singularity in a vacuum, asymptotically flat spacetime would be a clear violation of cosmic censorship. We find initial value solutions to Einstein's field equations that may lead to this behavior. We construct two families of asymptotically flat, axisymmetric vaccum solutions at a moment of time symmetry. The limiting members of these families are singular. Our first family represents a linear string of Schwarzschild black holes. We study the divergence of the gravitational tidal field outside the holes as their number along the string is increased. Our second family consists of prolate Brill gravitational wave packets. We examine the tidal field strength as the characteristic width of the wave is reduced towards zero. In both cases we find that configurations can be constructed with arbitrarily large fields that are not clothed by apparent horizons. These configurations are characterized by long, prolate concentrations of mass energy. We analyze our results in the context of the hoop conjecture
- …