965 research outputs found
A Linear-Nonlinear Formulation of Einstein Equations for the Two-Body Problem in General Relativity
A formulation of Einstein equations is presented that could yield advantages
in the study of collisions of binary compact objects during regimes between
linear-nonlinear transitions. The key idea behind this formulation is a
separation of the dynamical variables into i) a fixed conformal 3-geometry, ii)
a conformal factor possessing nonlinear dynamics and iii) transverse-traceless
perturbations of the conformal 3-geometry.Comment: 7 pages, no figure
Relativistic dust disks and the Wilson-Mathews approach
Treating problems in full general relativity is highly complex and frequently
approximate methods are employed to simplify the solution. We present
comparative solutions of a infinitesimally thin relativistic, stationary,
rigidly rotating disk obtained using the full equations and the approximate
approach suggested by Wilson & Mathews. We find that the Wilson-Mathews method
has about the same accuracy as the first post-Newtonian approximation.Comment: 4 Pages, 5 eps-figures, uses revtex.sty. Submitted to PR
Irrotational binary neutron stars in quasiequilibrium
We report on numerical results from an independent formalism to describe the
quasi-equilibrium structure of nonsynchronous binary neutron stars in general
relativity. This is an important independent test of controversial numerical
hydrodynamic simulations which suggested that nonsynchronous neutron stars in a
close binary can experience compression prior to the last stable circular
orbit. We show that, for compact enough stars the interior density increases
slightly as irrotational binary neutron stars approach their last orbits. The
magnitude of the effect, however, is much smaller than that reported in
previous hydrodynamic simulations.Comment: 4 pages, 2 figures, revtex, accepted for publication in Phys. Rev.
Relativistic Models for Binary Neutron Stars with Arbitrary Spins
We introduce a new numerical scheme for solving the initial value problem for
quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled
Einstein field equations and equations of relativistic hydrodynamics are solved
in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences
of circular-orbit binaries of varying separation, keeping the rest mass and
circulation constant along each sequence. Solutions are presented for
configurations obeying an n=1 polytropic equation of state and spinning
parallel and antiparallel to the orbital angular momentum. We treat stars with
moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all
but the highest circulation sequences, the spins of the neutron stars increase
as the binary separation decreases. Our zero-circulation cases approximate
irrotational sequences, for which the spin angular frequencies of the stars
increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19)
by the time the innermost circular orbit is reached. In addition to leaving an
imprint on the inspiral gravitational waveform, this spin effect is measurable
in the electromagnetic signal if one of the stars is a pulsar visible from
Earth.Comment: 21 pages, 14 figures. A few explanatory sentences added and some
typos corrected. Accepted for publication in Phys. Rev.
Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity
This paper reports on our effort in modeling realistic astrophysical neutron
star binaries in general relativity. We analyze under what conditions the
conformally flat quasiequilibrium (CFQE) approach can generate
``astrophysically relevant'' initial data, by developing an analysis that
determines the violation of the CFQE approximation in the evolution of the
binary described by the full Einstein theory. We show that the CFQE assumptions
significantly violate the Einstein field equations for corotating neutron stars
at orbital separations nearly double that of the innermost stable circular
orbit (ISCO) separation, thus calling into question the astrophysical relevance
of the ISCO determined in the CFQE approach. With the need to start numerical
simulations at large orbital separation in mind, we push for stable and long
term integrations of the full Einstein equations for the binary neutron star
system. We demonstrate the stability of our numerical treatment and analyze the
stringent requirements on resolution and size of the computational domain for
an accurate simulation of the system.Comment: 22 pages, 18 figures, accepted to Phys. Rev.
Gauge conditions for binary black hole puncture data based on an approximate helical Killing vector
We show that puncture data for quasicircular binary black hole orbits allow a
special gauge choice that realizes some of the necessary conditions for the
existence of an approximate helical Killing vector field. Introducing free
parameters for the lapse at the punctures we can satisfy the condition that the
Komar and ADM mass agree at spatial infinity. Several other conditions for an
approximate Killing vector are then automatically satisfied, and the 3-metric
evolves on a timescale smaller than the orbital timescale. The time derivative
of the extrinsic curvature however remains significant. Nevertheless,
quasicircular puncture data are not as far from possessing a helical Killing
vector as one might have expected.Comment: 11 pages, 6 figures, 2 table
Ice cloud processing of ultra-viscous/glassy aerosol particles leads to enhanced ice nucleation ability
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
Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars
This is the second in a series of papers on the construction and validation
of a three-dimensional code for the solution of the coupled system of the
Einstein equations and of the general relativistic hydrodynamic equations, and
on the application of this code to problems in general relativistic
astrophysics. In particular, we report on the accuracy of our code in the
long-term dynamical evolution of relativistic stars and on some new physics
results obtained in the process of code testing. The tests involve single
non-rotating stars in stable equilibrium, non-rotating stars undergoing radial
and quadrupolar oscillations, non-rotating stars on the unstable branch of the
equilibrium configurations migrating to the stable branch, non-rotating stars
undergoing gravitational collapse to a black hole, and rapidly rotating stars
in stable equilibrium and undergoing quasi-radial oscillations. The numerical
evolutions have been carried out in full general relativity using different
types of polytropic equations of state using either the rest-mass density only,
or the rest-mass density and the internal energy as independent variables. New
variants of the spacetime evolution and new high resolution shock capturing
(HRSC) treatments based on Riemann solvers and slope limiters have been
implemented and the results compared with those obtained from previous methods.
Finally, we have obtained the first eigenfrequencies of rotating stars in full
general relativity and rapid rotation. A long standing problem, such
frequencies have not been obtained by other methods. Overall, and to the best
of our knowledge, the results presented in this paper represent the most
accurate long-term three-dimensional evolutions of relativistic stars available
to date.Comment: 19 pages, 17 figure
Conformal-thin-sandwich initial data for a single boosted or spinning black hole puncture
Sequences of initial-data sets representing binary black holes in
quasi-circular orbits have been used to calculate what may be interpreted as
the innermost stable circular orbit. These sequences have been computed with
two approaches. One method is based on the traditional
conformal-transverse-traceless decomposition and locates quasi-circular orbits
from the turning points in an effective potential. The second method uses a
conformal-thin-sandwich decomposition and determines quasi-circular orbits by
requiring the existence of an approximate helical Killing vector. Although the
parameters defining the innermost stable circular orbit obtained from these two
methods differ significantly, both approaches yield approximately the same
initial data, as the separation of the binary system increases. To help
understanding this agreement between data sets, we consider the case of initial
data representing a single boosted or spinning black hole puncture of the
Bowen-York type and show that the conformal-transverse-traceless and
conformal-thin-sandwich methods yield identical data, both satisfying the
conditions for the existence of an approximate Killing vector.Comment: 13 pages, 2 figure
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