1,492 research outputs found
Codimension-two critical behavior in vacuum gravitational collapse
We consider the critical behavior at the threshold of black hole formation
for the five dimensional vacuum Einstein equations satisfying the
cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry
present in this model we predict the existence of a codimension-two attractor.
This prediction is confirmed numerically and the codimension-two attractor is
identified as a discretely self-similar solution with two unstable modes.Comment: 4 pages, 5 figures, typos correcte
Scaling of curvature in sub-critical gravitational collapse
We perform numerical simulations of the gravitational collapse of a
spherically symmetric scalar field. For those data that just barely do not form
black holes we find the maximum curvature at the position of the central
observer. We find a scaling relation between this maximum curvature and
distance from the critical solution. The scaling relation is analogous to that
found by Choptuik for black hole mass for those data that do collapse to form
black holes. We also find a periodic wiggle in the scaling exponent.Comment: Revtex, 2 figures, Discussion modified, to appear in Phys. Rev.
High Sensitivity Torsion Balance Tests for LISA Proof Mass Modeling
We have built a highly sensitive torsion balance to investigate small forces
between closely spaced gold coated surfaces. Such forces will occur between the
LISA proof mass and its housing. These forces are not well understood and
experimental investigations are imperative. We describe our torsion balance and
present the noise of the system. A significant contribution to the LISA noise
budget at low frequencies is the fluctuation in the surface potential
difference between the proof mass and its housing. We present first results of
these measurements with our apparatus.Comment: 6th International LISA Symposiu
Test of the Equivalence Principle Using a Rotating Torsion Balance
We used a continuously rotating torsion balance instrument to measure the
acceleration difference of beryllium and titanium test bodies towards sources
at a variety of distances. Our result Delta a=(0.6+/-3.1)x10^-15 m/s^2 improves
limits on equivalence-principle violations with ranges from 1 m to infinity by
an order of magnitude. The Eoetvoes parameter is eta=(0.3+/-1.8)x10^-13. By
analyzing our data for accelerations towards the center of the Milky Way we
find equal attractions of Be and Ti towards galactic dark matter, yielding
eta=(-4 +/- 7)x10^-5. Space-fixed differential accelerations in any direction
are limited to less than 8.8x10^-15 m/s^2 with 95% confidence.Comment: 4 pages, 4 figures; accepted for publication in PR
Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid
We observe critical phenomena in spherical collapse of radiation fluid. A
sequence of spacetimes is numerically computed, containing
models () that adiabatically disperse and models () that
form a black hole. Near the critical point (), evolutions develop a
self-similar region within which collapse is balanced by a strong,
inward-moving rarefaction wave that holds constant as a function of a
self-similar coordinate . The self-similar solution is known and we show
near-critical evolutions asymptotically approaching it. A critical exponent
is found for supercritical () models.Comment: 10 pages (LaTeX) (to appear in Phys. Rev. Lett.), TAR-039-UN
Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse
We study the critical behaviour of spherically symmetric scalar field
collapse to black holes in spacetime dimensions other than four. We obtain
reliable values for the scaling exponent in the supercritical region for
dimensions in the range . The critical exponent increases
monotonically to an asymptotic value at large of . The
data is well fit by a simple exponential of the form: .Comment: 5 pages, including 7 figures New version contains more data points,
one extra graph and more accurate error bars. No changes to result
Numerical stability for finite difference approximations of Einstein's equations
We extend the notion of numerical stability of finite difference
approximations to include hyperbolic systems that are first order in time and
second order in space, such as those that appear in Numerical Relativity. By
analyzing the symbol of the second order system, we obtain necessary and
sufficient conditions for stability in a discrete norm containing one-sided
difference operators. We prove stability for certain toy models and the
linearized Nagy-Ortiz-Reula formulation of Einstein's equations.
We also find that, unlike in the fully first order case, standard
discretizations of some well-posed problems lead to unstable schemes and that
the Courant limits are not always simply related to the characteristic speeds
of the continuum problem. Finally, we propose methods for testing stability for
second order in space hyperbolic systems.Comment: 18 pages, 9 figure
Domain wall interacting with a black hole: A new example of critical phenomena
We study a simple system that comprises all main features of critical
gravitational collapse, originally discovered by Choptuik and discussed in many
subsequent publications. These features include universality of phenomena,
mass-scaling relations, self-similarity, symmetry between super-critical and
sub-critical solutions, etc.
The system we consider is a stationary membrane (representing a domain wall)
in a static gravitational field of a black hole. For a membrane that spreads to
infinity, the induced 2+1 geometry is asymptotically flat. Besides solutions
with Minkowski topology there exists also solutions with the induced metric and
topology of a 2+1 dimensional black hole. By changing boundary conditions at
infinity, one finds that there is a transition between these two families. This
transition is critical and it possesses all the above-mentioned properties of
critical gravitational collapse. It is remarkable that characteristics of this
transition can be obtained analytically. In particular, we find exact
analytical expressions for scaling exponents and wiggle-periods.
Our results imply that black hole formation as a critical phenomenon is far
more general than one might expect.Comment: 23 pages, 5 postscript figures include
Late Time Tail of Wave Propagation on Curved Spacetime
The late time behavior of waves propagating on a general curved spacetime is
studied. The late time tail is not necessarily an inverse power of time. Our
work extends, places in context, and provides understanding for the known
results for the Schwarzschild spacetime. Analytic and numerical results are in
excellent agreement.Comment: 11 pages, WUGRAV-94-1
Radiative falloff in the background of rotating black hole
We study numerically the late-time tails of linearized fields with any spin
in the background of a spinning black hole. Our code is based on the
ingoing Kerr coordinates, which allow us to penetrate through the event
horizon. The late time tails are dominated by the mode with the least multipole
moment which is consistent with the equatorial symmetry of the initial
data and is equal to or greater than the least radiative mode with and the
azimuthal number .Comment: 5 pages, 4 Encapsulated PostScript figures; Accepted to Phys. Rev. D
(Rapid Communication
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