1,371 research outputs found
Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
Several numerical relativity groups are using a modified ADM formulation for
their simulations, which was developed by Nakamura et al (and widely cited as
Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is
shown to be more stable than the standard ADM formulation in many cases, and
there have been many attempts to explain why this re-formulation has such an
advantage. We try to explain the background mechanism of the BSSN equations by
using eigenvalue analysis of constraint propagation equations. This analysis
has been applied and has succeeded in explaining other systems in our series of
works. We derive the full set of the constraint propagation equations, and
study it in the flat background space-time. We carefully examine how the
replacements and adjustments in the equations change the propagation structure
of the constraints, i.e. whether violation of constraints (if it exists) will
decay or propagate away. We conclude that the better stability of the BSSN
system is obtained by their adjustments in the equations, and that the
combination of the adjustments is in a good balance, i.e. a lack of their
adjustments might fail to obtain the present stability. We further propose
other adjustments to the equations, which may offer more stable features than
the current BSSN equations.Comment: 10 pages, RevTeX4, added related discussion to gr-qc/0209106, the
version to appear in Phys. Rev.
Fate of Kaluza-Klein Bubble
We numerically study classical time evolutions of Kaluza-Klein bubble
space-time which has negative energy after a decay of vacuum. As the zero
energy Witten's bubble space-time, where the bubble expands infinitely, the
subsequent evolutions of Brill and Horowitz's momentarily static initial data
show that the bubble will expand in terms of the area. At first glance, this
result may support Corley and Jacobson's conjecture that the bubble will expand
forever as well as the Witten's bubble. The irregular signatures, however, can
be seen in the behavior of the lapse function in the maximal slicing gauge and
the divergence of the Kretchman invariant. Since there is no appearance of the
apparent horizon, we suspect an appearance of a naked singularity as the final
fate of this space-time.Comment: 13 pages including 10 figures, RevTeX, epsf.sty. CGPG-99/12-8,
RESCEU-6/00 and DAMTP-2000-30. To appear in Phys. Rev.
Finding Principal Null Direction for Numerical Relativists
We present a new method for finding principal null directions (PNDs). Because
our method assumes as input the intrinsic metric and extrinsic curvature of a
spacelike hypersurface, it should be particularly useful to numerical
relativists. We illustrate our method by finding the PNDs of the
Kastor-Traschen spacetimes, which contain arbitrarily many black holes in
a de Sitter back-ground.Comment: 10 pages, LaTeX style, WU-AP/38/93. Figures are available (hard
copies) upon requests [[email protected] (H.Shinkai)
Algebraic stability analysis of constraint propagation
The divergence of the constraint quantities is a major problem in
computational gravity today. Apparently, there are two sources for constraint
violations. The use of boundary conditions which are not compatible with the
constraint equations inadvertently leads to 'constraint violating modes'
propagating into the computational domain from the boundary. The other source
for constraint violation is intrinsic. It is already present in the initial
value problem, i.e. even when no boundary conditions have to be specified. Its
origin is due to the instability of the constraint surface in the phase space
of initial conditions for the time evolution equations. In this paper, we
present a technique to study in detail how this instability depends on gauge
parameters. We demonstrate this for the influence of the choice of the time
foliation in context of the Weyl system. This system is the essential
hyperbolic part in various formulations of the Einstein equations.Comment: 25 pages, 5 figures; v2: small additions, new reference, publication
number, classification and keywords added, address fixed; v3: update to match
journal versio
A trick for passing degenerate points in Ashtekar formulation
We examine one of the advantages of Ashtekar's formulation of general
relativity: a tractability of degenerate points from the point of view of
following the dynamics of classical spacetime. Assuming that all dynamical
variables are finite, we conclude that an essential trick for such a continuous
evolution is in complexifying variables. In order to restrict the complex
region locally, we propose some `reality recovering' conditions on spacetime.
Using a degenerate solution derived by pull-back technique, and integrating the
dynamical equations numerically, we show that this idea works in an actual
dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style
file are include
Boundary conditions for hyperbolic formulations of the Einstein equations
In regards to the initial-boundary value problem of the Einstein equations,
we argue that the projection of the Einstein equations along the normal to the
boundary yields necessary and appropriate boundary conditions for a wide class
of equivalent formulations. We explicitly show that this is so for the
Einstein-Christoffel formulation of the Einstein equations in the case of
spherical symmetry.Comment: 15 pages; text added and typesetting errors corrected; to appear in
Classical and Quantum Gravit
Semiclassical instability of the brane-world: Randall-Sundrum bubbles
We discuss the semiclassical instability of the Randall-Sundrum brane-world
model against a creation of a kind of Kaluza-Klein bubble. An example
describing such a bubble space-time is constructed from the five-dimensional
AdS-Schwarzschild metric. The induced geometry of the brane looks like the
Einstein-Rosen bridge, which connects the positive and the negative tension
branes. The bubble rapidly expands and there also form a trapped region around
it.Comment: 4 pages, 3 figures, two references adde
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