5,995 research outputs found
Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method
We present a new numerical scheme to solve the initial value problem for
black hole-neutron star binaries. This method takes advantage of the
flexibility and fast convergence of a multidomain spectral representation of
the initial data to construct high-accuracy solutions at a relatively low
computational cost. We provide convergence tests of the method for both
isolated neutron stars and irrotational binaries. In the second case, we show
that we can resolve the small inconsistencies that are part of the
quasi-equilibrium formulation, and that these inconsistencies are significantly
smaller than observed in previous works. The possibility of generating a wide
variety of initial data is also demonstrated through two new configurations
inspired by results from binary black holes. First, we show that choosing a
modified Kerr-Schild conformal metric instead of a flat conformal metric allows
for the construction of quasi-equilibrium binaries with a spinning black hole.
Second, we construct binaries in low-eccentricity orbits, which are a better
approximation to astrophysical binaries than quasi-equilibrium systems.Comment: 19 pages, 11 figures, Modified to match final PRD versio
Issues for the Next Generation of Galaxy Surveys
I argue that the weight of the available evidence favours the conclusions
that galaxies are unbiased tracers of mass, the mean mass density (excluding a
cosmological constant or its equivalent) is less than the critical Einstein-de
Sitter value, and an isocurvature model for structure formation offers a viable
and arguably attractive model for the early assembly of galaxies. If valid
these conclusions complicate our work of adding structure formation to the
standard model for cosmology, but it seems sensible to pay attention to
evidence.Comment: 14 pages, 3 postscript figures, uses rspublic.st
Noether symmetry approach in phantom quintessence cosmology
In the framework of phantom quintessence cosmology, we use the Noether
Symmetry Approach to obtain general exact solutions for the cosmological
equations. This result is achieved by the quintessential (phantom) potential
determined by the existence of the symmetry itself. A comparison between the
theoretical model and observations is worked out. In particular, we use type Ia
supernovae and large scale structure parameters determined from the 2-degree
Field Galaxy Redshift Survey (2dFGRS)and from the Wide part of the VIMOS-VLT
Deep Survey (VVDS). It turns out that the model is compatible with the
presently available observational data. Moreover we extend the approach to
include radiation. We show that it is compatible with data derived from
recombination and it seems that quintessence do not affect nucleosynthesis
results.Comment: 26 pages, 13 figure
Extrinsic Curvature and the Einstein Constraints
The Einstein initial-value equations in the extrinsic curvature (Hamiltonian)
representation and conformal thin sandwich (Lagrangian) representation are
brought into complete conformity by the use of a decomposition of symmetric
tensors which involves a weight function. In stationary spacetimes, there is a
natural choice of the weight function such that the transverse traceless part
of the extrinsic curvature (or canonical momentum) vanishes.Comment: 8 pages, no figures; added new section; significant polishing of tex
Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity
The accuracy and stability of the Caltech-Cornell pseudospectral code is
evaluated using the KST representation of the Einstein evolution equations. The
basic "Mexico City Tests" widely adopted by the numerical relativity community
are adapted here for codes based on spectral methods. Exponential convergence
of the spectral code is established, apparently limited only by numerical
roundoff error. A general expression for the growth of errors due to finite
machine precision is derived, and it is shown that this limit is achieved here
for the linear plane-wave test. All of these tests are found to be stable,
except for simulations of high amplitude gauge waves with nontrivial shift.Comment: Final version, as published in Phys. Rev. D; 13 pages, 16 figure
Scale-invariant gravity: Spacetime recovered
The configuration space of general relativity is superspace - the space of
all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued
that the configuration space for gravity should be conformal superspace - the
space of all Riemannian 3-metrics modulo diffeomorphisms and conformal
transformations. Recently a manifestly 3-dimensional theory was constructed
with conformal superspace as the configuration space. Here a fully
4-dimensional action is constructed so as to be invariant under conformal
transformations of the 4-metric using general relativity as a guide. This
action is then decomposed to a (3+1)-dimensional form and from this to its
Jacobi form. The surprising thing is that the new theory turns out to be
precisely the original 3-dimensional theory. The physical data is identified
and used to find the physical representation of the theory. In this
representation the theory is extremely similar to general relativity. The
clarity of the 4-dimensional picture should prove very useful for comparing the
theory with those aspects of general relativity which are usually treated in
the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex
Initial Data and Coordinates for Multiple Black Hole Systems
We present here an alternative approach to data setting for spacetimes with
multiple moving black holes generalizing the Kerr-Schild form for rotating or
non-rotating single black holes to multiple moving holes. Because this scheme
preserves the Kerr-Schild form near the holes, it selects out the behaviour of
null rays near the holes, may simplify horizon tracking, and may prove useful
in computational applications. For computational evolution, a discussion of
coordinates (lapse function and shift vector) is given which preserves some of
the properties of the single-hole Kerr-Schild form
Corotating and irrotational binary black holes in quasi-circular orbits
A complete formalism for constructing initial data representing black-hole
binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in
general, true equilibrium binary configurations. However, when the timescale
for orbital decay is much longer than the orbital period, a binary can be
considered to be in quasi-equilibrium. If each black hole is assumed to be in
quasi-equilibrium, then a complete set of boundary conditions for all initial
data variables can be developed. These boundary conditions are applied on the
apparent horizon of each black hole, and in fact force a specified surface to
be an apparent horizon. A global assumption of quasi-equilibrium is also used
to fix some of the freely specifiable pieces of the initial data and to
uniquely fix the asymptotic boundary conditions. This formalism should allow
for the construction of completely general quasi-equilibrium black hole binary
initial data.Comment: 13 pages, no figures, revtex4; Content changed slightly to reflect
fact that regularized shift solutions do satisfy the isometry boundary
condition
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