385 research outputs found
Gravitational Wavetrains in the Quasi-Equilibrium Approximation: A Model Problem in Scalar Gravitation
A quasi-equilibrium (QE) computational scheme was recently developed in
general relativity to calculate the complete gravitational wavetrain emitted
during the inspiral phase of compact binaries. The QE method exploits the fact
that the the gravitational radiation inspiral timescale is much longer than the
orbital period everywhere outside the ISCO. Here we demonstrate the validity
and advantages of the QE scheme by solving a model problem in relativistic
scalar gravitation theory. By adopting scalar gravitation, we are able to
numerically track without approximation the damping of a simple, quasi-periodic
radiating system (an oscillating spherical matter shell) to final equilibrium,
and then use the exact numerical results to calibrate the QE approximation
method. In particular, we calculate the emitted gravitational wavetrain three
different ways: by integrating the exact coupled dynamical field and matter
equations, by using the scalar-wave monopole approximation formula
(corresponding to the quadrupole formula in general relativity), and by
adopting the QE scheme. We find that the monopole formula works well for weak
field cases, but fails when the fields become even moderately strong. By
contrast, the QE scheme remains quite reliable for moderately strong fields,
and begins to breakdown only for ultra-strong fields. The QE scheme thus
provides a promising technique to construct the complete wavetrain from binary
inspiral outside the ISCO, where the gravitational fields are strong, but where
the computational resources required to follow the system for more than a few
orbits by direct numerical integration of the exact equations are prohibitive.Comment: 15 pages, 14 figure
Analytical Tendex and Vortex Fields for Perturbative Black Hole Initial Data
Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the
electric and magnetic parts of the Weyl curvature tensor, form the basis of a
recently developed approach to visualizing spacetime curvature. In particular,
this method has been proposed as a tool for interpreting results from numerical
binary black hole simulations, providing a deeper insight into the physical
processes governing the merger of black holes and the emission of gravitational
radiation. Here we apply this approach to approximate but analytical initial
data for both single boosted and binary black holes. These perturbative data
become exact in the limit of small boost or large binary separation. We hope
that these calculations will provide additional insight into the properties of
tendex and vortex fields, and will form a useful test for future numerical
calculations.Comment: 18 pages, 8 figures, submitted to PR
Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test
We include matter sources in Einstein's field equations and show that our
recently proposed 3+1 evolution scheme can stably evolve strong-field
solutions. We insert in our code known matter solutions, namely the
Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder
solution for homogeneous dust sphere collapse to a black hole, and evolve the
gravitational field equations. We find that we can evolve stably static,
strong-field stars for arbitrarily long times and can follow dust sphere
collapse accurately well past black hole formation. These tests are useful
diagnostics for fully self-consistent, stable hydrodynamical simulations in 3+1
general relativity. Moreover, they suggest a successive approximation scheme
for determining gravitational waveforms from strong-field sources dominated by
longitudinal fields, like binary neutron stars: approximate quasi-equilibrium
models can serve as sources for the transverse field equations, which can be
evolved without having to re-solve the hydrodynamical equations (``hydro
without hydro'').Comment: 4 postscript figures. Submitted to Phys. Rev. D15 as a Brief Repor
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
Emergence of thin shell structure during collapse in isotropic coordinates
Numerical studies of gravitational collapse in isotropic coordinates have
recently shown an interesting connection between the gravitational Lagrangian
and black hole thermodynamics. A study of the actual spacetime was not the main
focus of this work and in particular, the rich and interesting structure of the
interior has not been investigated in much detail and remains largely unknown.
We elucidate its features by performing a numerical study of the spacetime in
isotropic coordinates during gravitational collapse of a massless scalar field.
The most salient feature to emerge is the formation of a thin shell of matter
just inside the apparent horizon. The energy density and Ricci scalar peak at
the shell and there is a jump discontinuity in the extrinsic curvature across
the apparent horizon, the hallmark that a thin shell is present in its
vicinity. At late stages of the collapse, the spacetime consists of two vacuum
regions separated by the thin shell. The interior is described by an
interesting collapsing isotropic universe. It tends towards a vacuum (never
reaches a perfect vacuum) and there is a slight inhomogeneity in the interior
that plays a crucial role in the collapse process as the areal radius tends to
zero. The spacetime evolves towards a curvature (physical) singularity in the
interior, both a Weyl and Ricci singularity. In the exterior, our numerical
results match closely the analytical form of the Schwarzschild metric in
isotropic coordinates, providing a strong test of our numerical code.Comment: 24 pages, 10 figures. version to appear in Phys. Rev.
Towards a wave--extraction method for numerical relativity: III. Analytical examples for the Beetle--Burko radiation scalar
Beetle and Burko recently introduced a background--independent scalar
curvature invariant for general relativity that carries information only about
the gravitational radiation in generic spacetimes, in cases where such
radiation is incontrovertibly defined. In this paper we adopt a formalism that
only uses spatial data as they are used in numerical relativity and compute the
Beetle--Burko radiation scalar for a number of analytical examples,
specifically linearized Einstein--Rosen cylindrical waves, linearized
quadrupole waves, the Kerr spacetime, Bowen--York initial data, and the Kasner
spacetime. These examples illustrate how the Beetle--Burko radiation scalar can
be used to examine the gravitational wave content of numerically generated
spacetimes, and how it may provide a useful diagnostic for initial data sets.Comment: 23 pages, 4 figures; We changed the convention used, corrected typos,
and expanded the discussio
Possible explanation for star-crushing effect in binary neutron star simulations
A possible explanation is suggested for the controversial star-crushing
effect seen in numerical simulations of inspiraling neutron star binaries by
Wilson, Mathews and Marronetti (WMM). An apparently incorrect definition of
momentum density in the momentum constraint equation used by WMM gives rise to
a post-1-Newtonian error in the approximation scheme. We show by means of an
analytic, post-1-Newtonian calculation that this error causes an increase of
the stars' central densities which is of the order of several percent when the
stars are separated by a few stellar radii, in agreement with what is seen in
the simulations.Comment: 4 pages, 1 figure, uses revetx macros, minor revision
The Moment of Inertia of the Binary Pulsar J0737-3039A: Constraining the Nuclear Equation of State
We construct numerical models of the newly discovered binary pulsar
J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium
code that handles arbitrary spins and in the relativistic, slow-rotation
approximation. We compare results for a representative sample of viable nuclear
equations of state (EOS) that span three, qualitatively different, classes of
models for the description of nuclear matter. A future dynamical measurement of
the neutron star's moment of inertia from pulsar timing data will impose
significant constraints on the nuclear EOS. Even a moderately accurate
measurement (<~ 10 %) may be able to rule out some of these competing classes.
Using the measured mass, spin and moment of inertia to identify the optimal
model computed from different EOSs, one can determine the pulsar's radius.Comment: 4 pages, ApJL in pres
Stability of coalescing binary stars against gravitational collapse: hydrodynamical simulations
We perform simulations of relativistic binary stars in post-Newtonian gravity
to investigate their dynamical stability prior to merger against gravitational
collapse in a tidal field. In general, our equations are only strictly accurate
to first post-Newtonian order, but they recover full general relativity for
spherical, static stars. We study both corotational and irrotational binary
configurations of identical stars in circular orbits. We adopt a soft,
adiabatic equation of state with , for which the onset of
instability occurs at a sufficiently small value of the compaction that a
post-Newtonian approximation is quite accurate. For such a soft equation of
state there is no innermost stable circular orbit, so that we can study
arbitrarily close binaries. This choice still allows us to study all the
qualitative features exhibited by any adiabatic equation of state regarding
stability against gravitational collapse. We demonstrate that, independent of
the internal stellar velocity profile, the tidal field from a binary companion
stabilizes a star against gravitational collapse.Comment: 13 pages, 10 figures, RevTex, to appear in Phys. Rev.
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