79 research outputs found
Critical behavior of gravitating sphalerons
We examine the gravitational collapse of sphaleron type configurations in
Einstein--Yang--Mills--Higgs theory. Working in spherical symmetry, we
investigate the critical behavior in this model. We provide evidence that for
various initial configurations, there can be three different critical
transitions between possible endstates with different critical solutions
sitting on the threshold between these outcomes. In addition, we show that
within the dispersive and black hole regimes, there are new possible endstates,
namely a stable, regular sphaleron and a stable, hairy black hole.Comment: Latex, 14 pages, 8 figure
Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry
We perform a numerical study of the critical regime at the threshold of black
hole formation in the spherically symmetric, general relativistic collapse of
collisionless matter. The coupled Einstein-Vlasov equations are solved using a
particle-mesh method in which the evolution of the phase-space distribution
function is approximated by a set of particles (or, more precisely,
infinitesimally thin shells) moving along geodesics of the spacetime.
Individual particles may have non-zero angular momenta, but spherical symmetry
dictates that the total angular momentum of the matter distribution vanish. In
accord with previous work by Rein et al, our results indicate that the critical
behavior in this model is Type I; that is, the smallest black hole in each
parametrized family has a finite mass. We present evidence that the critical
solutions are characterized by unstable, static spacetimes, with non-trivial
distributions of radial momenta for the particles. As expected for Type I
solutions, we also find power-law scaling relations for the lifetimes of
near-critical configurations as a function of parameter-space distance from
criticality.Comment: 32 pages, 10 figure
Remark on formation of colored black holes via fine tuning
In a recent paper (gr-qc/9903081) Choptuik, Hirschmann, and Marsa have
discovered the scaling law for the lifetime of an intermediate attractor in the
formation of n=1 colored black holes via fine tuning. We show that their result
is in agreement with the prediction of linear perturbation analysis. We also
briefly comment on the dependence of the mass gap across the threshold on the
radius of the event horizon.Comment: 2 pages, RevTex, 2 postscript figure
Adaptive Mesh Refinement for Characteristic Grids
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when
numerically solving partial differential equations with wave-like solutions,
using characteristic (double-null) grids. Such AMR algorithms are naturally
recursive, and the best-known past Berger-Oliger characteristic AMR algorithm,
that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on
individual "diamond" characteristic grid cells. This leads to the use of
fine-grained memory management, with individual grid cells kept in
2-dimensional linked lists at each refinement level. This complicates the
implementation and adds overhead in both space and time.
Here I describe a Berger-Oliger characteristic AMR algorithm which instead
recurses on null \emph{slices}. This algorithm is very similar to the usual
Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory
management, allowing entire null slices to be stored in contiguous arrays in
memory. The algorithm is very efficient in both space and time.
I describe discretizations yielding both 2nd and 4th order global accuracy.
My code implementing the algorithm described here is included in the electronic
supplementary materials accompanying this paper, and is freely available to
other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are
viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3
document class, includes C++ source code. Changes from v1: revised in
response to referee comments: many references added, new figure added to
better explain the algorithm, other small changes, C++ code updated to latest
versio
New Critical Behavior in Einstein-Yang-Mills Collapse
We extend the investigation of the gravitational collapse of a spherically
symmetric Yang-Mills field in Einstein gravity and show that, within the black
hole regime, a new kind of critical behavior arises which separates black holes
formed via Type I collapse from black holes formed through Type II collapse.
Further, we provide evidence that these new attracting critical solutions are
in fact the previously discovered colored black holes with a single unstable
mode.Comment: 13 pages, 4 figure
Critical Collapse of the Massless Scalar Field in Axisymmetry
We present results from a numerical study of critical gravitational collapse
of axisymmetric distributions of massless scalar field energy. We find
threshold behavior that can be described by the spherically symmetric critical
solution with axisymmetric perturbations. However, we see indications of a
growing, non-spherical mode about the spherically symmetric critical solution.
The effect of this instability is that the small asymmetry present in what
would otherwise be a spherically symmetric self-similar solution grows. This
growth continues until a bifurcation occurs and two distinct regions form on
the axis, each resembling the spherically symmetric self-similar solution. The
existence of a non-spherical unstable mode is in conflict with previous
perturbative results, and we therefore discuss whether such a mode exists in
the continuum limit, or whether we are instead seeing a marginally stable mode
that is rendered unstable by numerical approximation.Comment: 11 pages, 8 figure
Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
This paper continues a study on Choptuik scaling in gravitational collapse of
a complex scalar field at the threshold for black hole formation. We perform a
linear perturbation analysis of the previously derived complex critical
solution, and calculate the critical exponent for black hole mass, . We also show that this critical solution is unstable via a
growing oscillatory mode.Comment: 15 pages of latex/revtex; added details of numerics, in press in Phys
Rev D; 1 figure included, or available by anonymous ftp to
ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-58.ep
Soap Bubbles in Outer Space: Interaction of a Domain Wall with a Black Hole
We discuss the generalized Plateau problem in the 3+1 dimensional
Schwarzschild background. This represents the physical situation, which could
for instance have appeared in the early universe, where a cosmic membrane (thin
domain wall) is located near a black hole. Considering stationary axially
symmetric membranes, three different membrane-topologies are possible depending
on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole
topology and 2+1 black hole topology.
Interestingly, we find that the different membrane-topologies are connected
via phase transitions of the form first discussed by Choptuik in investigations
of scalar field collapse. More precisely, we find a first order phase
transition (finite mass gap) between wormhole topology and black hole topology;
the intermediate membrane being an unstable wormhole collapsing to a black
hole. Moreover, we find a second order phase transition (no mass gap) between
Minkowski topology and black hole topology; the intermediate membrane being a
naked singularity.
For the membranes of black hole topology, we find a mass scaling relation
analogous to that originally found by Choptuik. However, in our case the
parameter is replaced by a 2-vector parametrizing the solutions.
We find that where . We also find a periodic wiggle in the scaling relation.
Our results show that black hole formation as a critical phenomenon is far
more general than expected.Comment: 15 pages, Latex, 4 figures include
The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement
Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1
Minkowski space to S^3, are computed in three spatial dimensions (3D) using
adaptive mesh refinement (AMR). For initial data with compact support the model
is known to have two regimes, one in which regular initial data forms a
singularity and another in which the energy is dispersed to infinity. The
transition between these regimes has been shown in spherical symmetry to
demonstrate threshold behavior similar to that between black hole formation and
dispersal in gravitating theories. Here, I generalize the result by removing
the assumption of spherical symmetry. The evolutions suggest that the
spherically symmetric critical solution remains an intermediate attractor
separating the two end states.Comment: 5 pages, 5 figures, 1 table; To be published in Phys. Rev. D.; Added
discussion of initial data; Added figure and reference
Generalized harmonic formulation in spherical symmetry
In this pedagogically structured article, we describe a generalized harmonic
formulation of the Einstein equations in spherical symmetry which is regular at
the origin. The generalized harmonic approach has attracted significant
attention in numerical relativity over the past few years, especially as
applied to the problem of binary inspiral and merger. A key issue when using
the technique is the choice of the gauge source functions, and recent work has
provided several prescriptions for gauge drivers designed to evolve these
functions in a controlled way. We numerically investigate the parameter spaces
of some of these drivers in the context of fully non-linear collapse of a real,
massless scalar field, and determine nearly optimal parameter settings for
specific situations. Surprisingly, we find that many of the drivers that
perform well in 3+1 calculations that use Cartesian coordinates, are
considerably less effective in spherical symmetry, where some of them are, in
fact, unstable.Comment: 47 pages, 15 figures. v2: Minor corrections, including 2 added
references; journal version
- …