269 research outputs found
Scale invariance and critical gravitational collapse
We examine ways to write the Choptuik critical solution as the evolution of
scale invariant variables. It is shown that a system of scale invariant
variables proposed by one of the authors does not evolve periodically in the
Choptuik critical solution. We find a different system, based on maximal
slicing. This system does evolve periodically, and may generalize to the case
of axisymmetry or of no symmetry at all.Comment: 7 pages, 3 figures, Revtex, discussion modified to clarify
presentatio
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.
Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves
We report on numerical simulations of critical phenomena near the threshold
of black hole formation in the collapse of axisymmetric gravitational waves in
vacuum. We discuss several new features of our numerical treatment, and then
compare results obtained from families of quadrupolar and hexadecapolar initial
data. Specifically, we construct (nonlinear) initial data from quadrupolar and
hexadecapolar, time-symmetric wavelike solutions to the linearized Einstein
equations (often referred to as Teukolsky waves), and evolve these using a
shock-avoiding slicing condition. While our degree of fine-tuning to the onset
of black-hole formation is rather modest, we identify several features of the
threshold solutions formed for the two families. Both threshold solutions
appear to display an at least approximate discrete self-similarity with an
accumulation event at the center, and the characteristics of the threshold
solution for the quadrupolar data are consistent with those found previously by
other authors. The hexadecapolar threshold solution appears to be distinct from
the quadrupolar one, providing further support to the notion that there is no
universal critical solution for the collapse of vacuum gravitational waves.Comment: 17 pages, 14 figure
On free evolution of self gravitating, spherically symmetric waves
We perform a numerical free evolution of a selfgravitating, spherically
symmetric scalar field satisfying the wave equation. The evolution equations
can be written in a very simple form and are symmetric hyperbolic in
Eddington-Finkelstein coordinates. The simplicity of the system allow to
display and deal with the typical gauge instability present in these
coordinates. The numerical evolution is performed with a standard method of
lines fourth order in space and time. The time algorithm is Runge-Kutta while
the space discrete derivative is symmetric (non-dissipative). The constraints
are preserved under evolution (within numerical errors) and we are able to
reproduce several known results.Comment: 15 pages, 15 figure
An exact solution for 2+1 dimensional critical collapse
We find an exact solution in closed form for the critical collapse of a
scalar field with cosmological constant in 2+1 dimensions. This solution agrees
with the numerical simulation done by Pretorius and Choptuik of this system.Comment: 5 pages, 5 figures, Revtex. New comparison of analytic and numerical
solutions beyond the past light cone of the singularity added. Two new
references added. Error in equation (21) correcte
Choptuik scaling in six dimensions
We perform numerical simulations of the critical gravitational collapse of a
spherically symmetric scalar field in 6 dimensions. The critical solution has
discrete self-similarity. We find the critical exponent \gamma and the
self-similarity period \Delta.Comment: 8 pages, 3 figures RevTe
Evolutions of Magnetized and Rotating Neutron Stars
We study the evolution of magnetized and rigidly rotating neutron stars
within a fully general relativistic implementation of ideal
magnetohydrodynamics with no assumed symmetries in three spatial dimensions.
The stars are modeled as rotating, magnetized polytropic stars and we examine
diverse scenarios to study their dynamics and stability properties. In
particular we concentrate on the stability of the stars and possible critical
behavior. In addition to their intrinsic physical significance, we use these
evolutions as further tests of our implementation which incorporates new
developments to handle magnetized systems.Comment: 12 pages, 8 figure
Critical collapse of a massive vector field
We perform numerical simulations of the critical gravitational collapse of a
massive vector field. The result is that there are two critical solutions. One
is equivalent to the Choptuik critical solution for a massless scalar field.
The other is periodic.Comment: 7 pages, 4 figure
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