1,160 research outputs found
Late-time evolution of nonlinear gravitational collapse
We study numerically the fully nonlinear gravitational collapse of a
self-gravitating, minimally-coupled, massless scalar field in spherical
symmetry. Our numerical code is based on double-null coordinates and on free
evolution of the metric functions: The evolution equations are integrated
numerically, whereas the constraint equations are only monitored. The numerical
code is stable (unlike recent claims) and second-order accurate. We use this
code to study the late-time asymptotic behavior at fixed (outside the black
hole), along the event horizon, and along future null infinity. In all three
asymptotic regions we find that, after the decay of the quasi-normal modes, the
perturbations are dominated by inverse power-law tails. The corresponding power
indices agree with the integer values predicted by linearized theory. We also
study the case of a charged black hole nonlinearly perturbed by a (neutral)
self-gravitating scalar field, and find the same type of behavior---i.e.,
quasi-normal modes followed by inverse power-law tails, with the same indices
as in the uncharged case.Comment: 14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new
convergence test and a determination of QN ringing were added, in addition to
correction of typos and update of reference
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
Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems: The Black Hole Regime
The Cauchy+characteristic matching (CCM) problem for the scalar wave equation
is investigated in the background geometry of a Schwarzschild black hole.
Previously reported work developed the CCM framework for the coupled
Einstein-Klein-Gordon system of equations, assuming a regular center of
symmetry. Here, the time evolution after the formation of a black hole is
pursued, using a CCM formulation of the governing equations perturbed around
the Schwarzschild background. An extension of the matching scheme allows for
arbitrary matching boundary motion across the coordinate grid. As a proof of
concept, the late time behavior of the dynamics of the scalar field is
explored. The power-law tails in both the time-like and null infinity limits
are verified.Comment: To appear in Phys. Rev. D, 9 pages, revtex, 5 figures available at
http://www.astro.psu.edu/users/nr/preprints.htm
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.
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
Asymptotic tails of massive scalar fields in Schwarzschild background
We investigate the asymptotic tail behavior of massive scalar fields in
Schwarzschild background. It is shown that the oscillatory tail of the scalar
field has the decay rate of at asymptotically late times, and the
oscillation with the period for the field mass is modulated by the
long-term phase shift. These behaviors are qualitatively similar to those found
in nearly extreme Reissner-Nordstr\"{o}m background, which are discussed in
terms of a resonant backscattering due to the space-time curvature.Comment: 21 pages, 2 figures, accepted for publication in Phys.Rev.
Dynamics of Scalar Fields in the Background of Rotating Black Holes
A numerical study of the evolution of a massless scalar field in the
background of rotating black holes is presented. First, solutions to the wave
equation are obtained for slowly rotating black holes. In this approximation,
the background geometry is treated as a perturbed Schwarzschild spacetime with
the angular momentum per unit mass playing the role of a perturbative
parameter. To first order in the angular momentum of the black hole, the scalar
wave equation yields two coupled one-dimensional evolution equations for a
function representing the scalar field in the Schwarzschild background and a
second field that accounts for the rotation. Solutions to the wave equation are
also obtained for rapidly rotating black holes. In this case, the wave equation
does not admit complete separation of variables and yields a two-dimensional
evolution equation. The study shows that, for rotating black holes, the late
time dynamics of a massless scalar field exhibit the same power-law behavior as
in the case of a Schwarzschild background independently of the angular momentum
of the black hole.Comment: 14 pages, RevTex, 6 Figure
Late-Time Tails in Gravitational Collapse of a Self-Interacting (Massive) Scalar-Field and Decay of a Self-Interacting Scalar Hair
We study analytically the initial value problem for a self-interacting
(massive) scalar-field on a Reissner-Nordstr\"om spacetime. Following the
no-hair theorem we examine the dynamical physical mechanism by which the
self-interacting (SI) hair decays. We show that the intermediate asymptotic
behaviour of SI perturbations is dominated by an oscillatory inverse power-law
decaying tail. We show that at late-times the decay of a SI hair is slower than
any power-law. We confirm our analytical results by numerical simulations.Comment: 16 pages, 3 ps figures, Revte
Phases of massive scalar field collapse
We study critical behavior in the collapse of massive spherically symmetric
scalar fields. We observe two distinct types of phase transition at the
threshold of black hole formation. Type II phase transitions occur when the
radial extent of the initial pulse is less than the Compton
wavelength () of the scalar field. The critical solution is that
found by Choptuik in the collapse of massless scalar fields. Type I phase
transitions, where the black hole formation turns on at finite mass, occur when
. The critical solutions are unstable soliton stars with
masses \alt 0.6 \mu^{-1}. Our results in combination with those obtained for
the collapse of a Yang-Mills field~{[M.~W. Choptuik, T. Chmaj, and P. Bizon,
Phys. Rev. Lett. 77, 424 (1996)]} suggest that unstable, confined solutions to
the Einstein-matter equations may be relevant to the critical point of other
matter models.Comment: 5 pages, RevTex, 4 postscript figures included using psfi
High-Order Contamination in the Tail of Gravitational Collapse
It is well known that the late-time behaviour of gravitational collapse is
{\it dominated} by an inverse power-law decaying tail. We calculate {\it
higher-order corrections} to this power-law behaviour in a spherically
symmetric gravitational collapse. The dominant ``contamination'' is shown to
die off at late times as . This decay rate is much {\it
slower} than has been considered so far. It implies, for instance, that an
`exact' (numerical) determination of the power index to within
requires extremely long integration times of order . We show that the
leading order fingerprint of the black-hole electric {\it charge} is of order
.Comment: 12 pages, 2 figure
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