1,862 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
Hamiltonian analysis of Poincar\'e gauge theory scalar modes
The Hamiltonian constraint formalism is used to obtain the first explicit
complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge
theory of gravity. Two modes with propagating spin-zero torsion are analyzed.
The explicit form of the Hamiltonian is presented. All constraints are obtained
and classified. The Lagrange multipliers are derived. It is shown that a
massive spin- mode has normal dynamical propagation but the associated
massless is pure gauge. The spin- mode investigated here is also
viable in general. Both modes exhibit a simple type of ``constraint
bifurcation'' for certain special field/parameter values.Comment: 28 pages, LaTex, submitted to International Journal of Modern Physics
Impact of densitized lapse slicings on evolutions of a wobbling black hole
We present long-term stable and second-order convergent evolutions of an
excised wobbling black hole. Our results clearly demonstrate that the use of a
densitized lapse function extends the lifetime of simulations dramatically. We
also show the improvement in the stability of single static black holes when an
algebraic densitized lapse condition is applied. In addition, we introduce a
computationally inexpensive approach for tracking the location of the
singularity suitable for mildly distorted black holes. The method is based on
investigating the fall-off behavior and asymmetry of appropriate grid
variables. This simple tracking method allows one to adjust the location of the
excision region to follow the coordinate motion of the singularity.Comment: 10 pages, 8 figure
Toward stable 3D numerical evolutions of black-hole spacetimes
Three dimensional (3D) numerical evolutions of static black holes with
excision are presented. These evolutions extend to about 8000M, where M is the
mass of the black hole. This degree of stability is achieved by using
growth-rate estimates to guide the fine tuning of the parameters in a
multi-parameter family of symmetric hyperbolic representations of the Einstein
evolution equations. These evolutions were performed using a fixed gauge in
order to separate the intrinsic stability of the evolution equations from the
effects of stability-enhancing gauge choices.Comment: 4 pages, 5 figures. To appear in Phys. Rev. D. Minor additions to
text for clarification. Added short paragraph about inner boundary dependenc
Comparing Criteria for Circular Orbits in General Relativity
We study a simple analytic solution to Einstein's field equations describing
a thin spherical shell consisting of collisionless particles in circular orbit.
We then apply two independent criteria for the identification of circular
orbits, which have recently been used in the numerical construction of binary
black hole solutions, and find that both yield equivalent results. Our
calculation illustrates these two criteria in a particularly transparent
framework and provides further evidence that the deviations found in those
numerical binary black hole solutions are not caused by the different criteria
for circular orbits.Comment: 4 pages; to appear in PRD as a Brief Report; added and corrected
reference
Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
The ability to control and tune interactions in ultracold atomic gases has
paved the way towards the realization of new phases of matter. Whereas
experiments have so far achieved a high degree of control over short-ranged
interactions, the realization of long-range interactions would open up a whole
new realm of many-body physics and has become a central focus of research.
Rydberg atoms are very well-suited to achieve this goal, as the van der Waals
forces between them are many orders of magnitude larger than for ground state
atoms. Consequently, the mere laser excitation of ultracold gases can cause
strongly correlated many-body states to emerge directly when atoms are
transferred to Rydberg states. A key example are quantum crystals, composed of
coherent superpositions of different spatially ordered configurations of
collective excitations. Here we report on the direct measurement of strong
correlations in a laser excited two-dimensional atomic Mott insulator using
high-resolution, in-situ Rydberg atom imaging. The observations reveal the
emergence of spatially ordered excitation patterns in the high-density
components of the prepared many-body state. They have random orientation, but
well defined geometry, forming mesoscopic crystals of collective excitations
delocalised throughout the gas. Our experiment demonstrates the potential of
Rydberg gases to realise exotic phases of matter, thereby laying the basis for
quantum simulations of long-range interacting quantum magnets.Comment: 10 pages, 7 figure
Mode coupling in the nonlinear response of black holes
We study the properties of the outgoing gravitational wave produced when a
non-spinning black hole is excited by an ingoing gravitational wave.
Simulations using a numerical code for solving Einstein's equations allow the
study to be extended from the linearized approximation, where the system is
treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime.
Several nonlinear features are found which bear importance to the data analysis
of gravitational waves. When compared to the results obtained in the linearized
approximation, we observe large phase shifts, a stronger than linear generation
of gravitational wave output and considerable generation of radiation in
polarization states which are not found in the linearized approximation. In
terms of a spherical harmonic decomposition, the nonlinear properties of the
harmonic amplitudes have simple scaling properties which offer an economical
way to catalog the details of the waves produced in such black hole processes.Comment: 17 pages, 20 figures, abstract and introduction re-writte
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.
- …