1,055 research outputs found
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
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
Binary Black Hole Mergers in 3d Numerical Relativity
The standard approach to the numerical evolution of black hole data using the
ADM formulation with maximal slicing and vanishing shift is extended to
non-symmetric black hole data containing black holes with linear momentum and
spin by using a time-independent conformal rescaling based on the puncture
representation of the black holes. We give an example for a concrete three
dimensional numerical implementation. The main result of the simulations is
that this approach allows for the first time to evolve through a brief period
of the merger phase of the black hole inspiral.Comment: 8 pages, 9 figures, REVTeX; expanded discussion, results unchange
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
Can Schwarzschildean gravitational fields suppress gravitational waves?
Gravitational waves in the linear approximation propagate in the
Schwarzschild spacetime similarly as electromagnetic waves. A fraction of the
radiation scatters off the curvature of the geometry. The energy of the
backscattered part of an initially outgoing pulse of the quadrupole
gravitational radiation is estimated by compact formulas depending on the
initial energy, the Schwarzschild radius, and the location and width of the
pulse. The backscatter becomes negligible in the short wavelength regime.Comment: 18 pages, Revtex. Added three references; a new comment in Sec. 7;
several misprints corrected. To appear in the Phys. Rev.
Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid
We observe critical phenomena in spherical collapse of radiation fluid. A
sequence of spacetimes is numerically computed, containing
models () that adiabatically disperse and models () that
form a black hole. Near the critical point (), evolutions develop a
self-similar region within which collapse is balanced by a strong,
inward-moving rarefaction wave that holds constant as a function of a
self-similar coordinate . The self-similar solution is known and we show
near-critical evolutions asymptotically approaching it. A critical exponent
is found for supercritical () models.Comment: 10 pages (LaTeX) (to appear in Phys. Rev. Lett.), TAR-039-UN
Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
We conducted three torsion-balance experiments to test the gravitational
inverse-square law at separations between 9.53 mm and 55 micrometers, probing
distances less than the dark-energy length scale m. We find with 95% confidence
that the inverse-square law holds () down to a length scale
m and that an extra dimension must have a size m.Comment: 4 pages, 6 figure
Strongly hyperbolic Hamiltonian systems in numerical relativity: Formulation and symplectic integration
We consider two strongly hyperbolic Hamiltonian formulations of general
relativity and their numerical integration with a free and a partially
constrained symplectic integrator. In those formulations we use hyperbolic
drivers for the shift and in one case also for the densitized lapse. A system
where the densitized lapse is an external field allows to enforce the momentum
constraints in a holonomically constrained Hamiltonian system and to turn the
Hamilton constraint function from a weak to a strong invariant.
These schemes are tested in a perturbed Minkowski and the Schwarzschild
space-time. In those examples we find advantages of the strongly hyperbolic
formulations over the ADM system presented in [arXiv:0807.0734]. Furthermore we
observe stabilizing effects of the partially constrained evolution in
Schwarzschild space-time as long as the momentum constraints are enforced.Comment: This version clarifies some points concerning the interpretation of
the result
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
Gravitino perturbations in Schwarzschild black holes
We consider the time evolution of massless gravitino perturbations in
Schwarzschild black holes, and show that as in the case of fields of other
values of spin, the evolution comes in three stages, after an initial outburst
as a first stage, we observe the damped oscillations characteristic of the
quasinormal ringing stage, followed by long time tails. Using the sixth order
WKB method and Prony fitting of time domain data we determine the quasinormal
frequencies. There is a good correspondence between the results obtained by the
above two methods, and we obtain a considerable improvement with respect to the
previously obtained third order WKB results. We also show that the response of
a black hole depends crucially on the spin class of the perturbing field: the
quality factor becomes a decreasing function of the spin for boson
perturbations, whereas the opposite situation appears for fermion ones
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