1,703 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
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.
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
Border of Spacetime
It is still uncertain whether the cosmic censorship conjecture is true or
not. To get a new insight into this issue, we propose the concept of the border
of spacetime as a generalization of the spacetime singularity and discuss its
visibility. The visible border, corresponding to the naked singularity, is not
only relevant to mathematical completeness of general relativity but also a
window into new physics in strongly curved spacetimes, which is in principle
observable.Comment: 4 pages, 1 figure, accepted for publication in Physical Review D,
typos correcte
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 extreme critical space-time: echoing and black-hole perturbations
A homothetic, static, spherically symmetric solution to the massless
Einstein- Klein-Gordon equations is described. There is a curvature singularity
which is central, null, bifurcate and marginally trapped. The space-time is
therefore extreme in the sense of lying at the threshold between black holes
and naked singularities, just avoiding both. A linear perturbation analysis
reveals two types of dominant mode. One breaks the continuous self-similarity
by periodic terms reminiscent of discrete self-similarity, with echoing period
within a few percent of the value observed numerically in near-critical
gravitational collapse. The other dominant mode explicitly produces a black
hole, white hole, eternally naked singularity or regular dispersal, the latter
indicating that the background is critical. The black hole is not static but
has constant area, the corresponding mass being linear in the perturbation
amplitudes, explicitly determining a unit critical exponent. It is argued that
a central null singularity may be a feature of critical gravitational collapse.Comment: 6 revtex pages, 6 eps figure
HUD Doesn\u27t Need New Legislative Authority to Better Integrate Climate Change Resilience into Its Disaster Recovery Program
This article examines the interaction between the Department of Housing and Urban Development (HUD)’s community development block grant disaster recovery program (CDBGDR) and the federal and state governments\u27 resilience and climate adaptation priorities. It identifies and analyzes the statutes that have guided HUD\u27s approach to date, by considering both key statutory language and legislative history. It also examines forms of soft guidance issued by HUD for use by various stakeholders, including both HUD CDBG-DR program officers and the state and local officials that interact with them. In reviewing this material, the article identifies a tension between the requirement that all projects funded by CDBG-DR tie back to the most recent disaster, and the logic of resilience, which holds that one should always build or rebuild with an eye to the next disaster. There are some signs of reconciliation: Rebuild By Design and the National Disaster Resilience Competition promote resilience to future disasters – at least in the context of recovery from Hurricane Sandy – and HUD appears to be taking action on climate change through its Climate Adaptation Plan and newly formed Climate Council. The article argues for carrying this potential reconciliation forward into future disaster recovery contexts and also into other HUD programs that relate in less obvious ways to disaster recovery and resilience to climate change, and proposes several ways the agency might do so
Dimensional Dependence of Black Hole Formation in Self-Similar Collapse of Scalar Field
We study classical and quantum self-similar collapses of a massless scalar
field in higher dimensions, and examine how the increase in the number of
dimensions affects gravitational collapse and black hole formation. Higher
dimensions seem to favor formation of black hole rather than other final
states, in that the initial data space for black hole formation enlarges as
dimension increases. On the other hand, the quantum gravity effect on the
collapse lessens as dimension increases. We also discuss the gravitational
collapse in a brane world with large but compact extra dimensions.Comment: Improved a few arguments and added a figur
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