118 research outputs found
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
On convergence towards a self-similar solution for a nonlinear wave equation - a case study
We consider the problem of asymptotic stability of a self-similar attractor
for a simple semilinear radial wave equation which arises in the study of the
Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In
the first step we determine the spectrum of linearized perturbations about the
attractor using a method of continued fractions. In the second step we
demonstrate numerically that the resulting eigensystem provides an accurate
description of the dynamics of convergence towards the attractor.Comment: 9 pages, 5 figure
On existence of mini-boson stars
We prove the existence of a countable family of globally regular solutions of
spherically symmetric Einstein-Klein-Gordon equations. These solutions, known
as mini-boson stars, were discovered numerically many years ago.Comment: 15 pages, 1 eps figure, LaTe
Equivariant wave maps exterior to a ball
We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps
from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed
analytical and numerical methods we show that, for a given topological degree
of the map, all solutions starting from smooth finite energy initial data
converge to the unique static solution (harmonic map). The asymptotics of this
relaxation process is described in detail. We hope that our model will provide
an attractive mathematical setting for gaining insight into
dissipation-by-dispersion phenomena, in particular the soliton resolution
conjecture.Comment: 16 pages, 9 figure
On blowup for Yang-Mills fields
We study development of singularities for the spherically symmetric
Yang-Mills equations in dimensional Minkowski spacetime for (the
critical dimension) and (the lowest supercritical dimension). Using
combined numerical and analytical methods we show in both cases that generic
solutions starting with sufficiently large initial data blow up in finite time.
The mechanism of singularity formation depends on the dimension: in the
blowup is exactly self-similar while in the blowup is only approximately
self-similar and can be viewed as the adiabatic shrinking of the marginally
stable static solution. The threshold for blowup and the connection with
critical phenomena in the gravitational collapse (which motivated this
research) are also briefly discussed.Comment: 4 pages, 3 figures, submitted to Physical Review Letter
On Equivalence of Critical Collapse of Non-Abelian Fields
We continue our study of the gravitational collapse of spherically symmetric
skyrmions. For certain families of initial data, we find the discretely
self-similar Type II critical transition characterized by the mass scaling
exponent and the echoing period . We
argue that the coincidence of these critical exponents with those found
previously in the Einstein-Yang-Mills model is not accidental but, in fact, the
two models belong to the same universality class.Comment: 7 pages, REVTex, 2 figures included, accepted for publication in
Physical Review
Self-similar solutions of semilinear wave equations with a focusing nonlinearity
We prove that in three space dimensions a nonlinear wave equation
with being an odd integer has a countable
family of regular spherically symmetric self-similar solutions.Comment: 12 pages, 3 figures, minor corrections to match the published versio
Self-similar Solutions of the Cubic Wave Equation
We prove that the focusing cubic wave equation in three spatial dimensions
has a countable family of self-similar solutions which are smooth inside the
past light cone of the singularity. These solutions are labeled by an integer
index which counts the number of oscillations of the solution. The
linearized operator around the -th solution is shown to have negative
eigenvalues (one of which corresponds to the gauge mode) which implies that all
solutions are unstable. It is also shown that all solutions have a
singularity outside the past light cone which casts doubt on whether these
solutions may participate in the Cauchy evolution, even for non-generic initial
data.Comment: 14 pages, 1 figur
Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime
We consider the Cauchy problem for a spherically symmetric SU(2) Yang-Mills
field propagating outside the Schwarzschild black hole. Although solutions
starting from smooth finite energy initial data remain smooth for all times,
not all of them scatter since there are non-generic solutions which
asymptotically tend to unstable static solutions. We show that a static
solution with one unstable mode appears as an intermediate attractor in the
evolution of initial data near a border between basins of attraction of two
different vacuum states. We study the saddle-point dynamics near this
attractor, in particular we identify the universal phases of evolution: the
ringdown approach, the exponential departure, and the eventual decay to one of
the vacuum states.Comment: 15 pages, 5 figure
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