372 research outputs found
Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
I study the Bona-Masso family of hyperbolic slicing conditions, considering
in particular its properties when approaching two different types of
singularities: focusing singularities and gauge shocks. For focusing
singularities, I extend the original analysis of Bona et. al and show that both
marginal and strong singularity avoidance can be obtained for certain types of
behavior of the slicing condition as the lapse approaches zero. For the case of
gauge shocks, I re-derive a condition found previously that eliminates them.
Unfortunately, such a condition limits considerably the type of slicings
allowed. However, useful slicing conditions can still be found if one asks for
this condition to be satisfied only approximately. Such less restrictive
conditions include a particular member of the 1+log family, which in the past
has been found empirically to be extremely robust for both Brill wave and black
hole simulations.Comment: 11 pages, revtex4. Change in acknowledgment
Gauge conditions for long-term numerical black hole evolutions without excision
Numerical relativity has faced the problem that standard 3+1 simulations of
black hole spacetimes without singularity excision and with singularity
avoiding lapse and vanishing shift fail after an evolution time of around
30-40M due to the so-called slice stretching. We discuss lapse and shift
conditions for the non-excision case that effectively cure slice stretching and
allow run times of 1000M and more.Comment: 19 pages, 14 figures, REVTeX, Added a missing Acknowledgmen
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.
An alternative approach to solving the Hamiltonian constraint
Solving Einstein's constraint equations for the construction of black hole
initial data requires handling the black hole singularity. Typically, this is
done either with the excision method, in which the black hole interior is
excised from the numerical grid, or with the puncture method, in which the
singular part of the conformal factor is expressed in terms of an analytical
background solution, and the Hamiltonian constraint is then solved for a
correction to the background solution that, usually, is assumed to be regular
everywhere. We discuss an alternative approach in which the Hamiltonian
constraint is solved for an inverse power of the conformal factor. This new
function remains finite everywhere, so that this approach requires neither
excision nor a split into background and correction. In particular, this method
can be used without modification even when the correction to the conformal
factor is singular itself. We demonstrate this feature for rotating black holes
in the trumpet topology.Comment: 5 pages, 4 figures, matches version published in PR
Quantum effects in the Alcubierre warp drive spacetime
The expectation value of the stress-energy tensor of a free conformally
invariant scalar field is computed in a two-dimensional reduction of the
Alcubierre ``warp drive'' spacetime. The stress-energy is found to diverge if
the apparent velocity of the spaceship exceeds the speed of light. If such
behavior occurs in four dimensions, then it appears implausible that ``warp
drive'' behavior in a spacetime could be engineered, even by an arbitrarily
advanced civilization.Comment: 9 pages, ReVTe
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