46 research outputs found
Circular orbits of corotating binary black holes: comparison between analytical and numerical results
We compare recent numerical results, obtained within a ``helical Killing
vector'' (HKV) approach, on circular orbits of corotating binary black holes to
the analytical predictions made by the effective one body (EOB) method (which
has been recently extended to the case of spinning bodies). On the scale of the
differences between the results obtained by different numerical methods, we
find good agreement between numerical data and analytical predictions for
several invariant functions describing the dynamical properties of circular
orbits. This agreement is robust against the post-Newtonian accuracy used for
the analytical estimates, as well as under choices of resummation method for
the EOB ``effective potential'', and gets better as one uses a higher
post-Newtonian accuracy. These findings open the way to a significant
``merging'' of analytical and numerical methods, i.e. to matching an EOB-based
analytical description of the (early and late) inspiral, up to the beginning of
the plunge, to a numerical description of the plunge and merger. We illustrate
also the ``flexibility'' of the EOB approach, i.e. the possibility of
determining some ``best fit'' values for the analytical parameters by
comparison with numerical data.Comment: Minor revisions, accepted for publication in Phys. Rev. D, 19 pages,
6 figure
Time-symmetric initial data for binary black holes in numerical relativity
We look for physically realistic initial data in numerical relativity which
are in agreement with post-Newtonian approximations. We propose a particular
solution of the time-symmetric constraint equation, appropriate to two
momentarily static black holes, in the form of a conformal decomposition of the
spatial metric. This solution is isometric to the post-Newtonian metric up to
the 2PN order. It represents a non-linear deformation of the solution of Brill
and Lindquist, i.e. an asymptotically flat region is connected to two
asymptotically flat (in a certain weak sense) sheets, that are the images of
the two singularities through appropriate inversion transformations. The total
ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are
computed by surface integrals performed at infinity. Using second order
perturbation theory on the Brill-Lindquist background, we prove that the
binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and
in agreement with the known post-Newtonian result.Comment: 27 pages, to appear in Phys. Rev.
A skeleton approximate solution of the Einstein field equations for multiple black-hole systems
An approximate analytical and non-linear solution of the Einstein field
equations is derived for a system of multiple non-rotating black holes. The
associated space-time has the same asymptotic structure as the Brill-Lindquist
initial data solution for multiple black holes. The system admits an
Arnowitt-Deser-Misner (ADM) Hamiltonian that can particularly evolve the
Brill-Lindquist solution over finite time intervals. The gravitational field of
this model may properly be referred to as a skeleton approximate solution of
the Einstein field equations. The approximation is based on a conformally flat
truncation, which excludes gravitational radiation, as well as a removal of
some additional gravitational field energy. After these two simplifications,
only source terms proportional to Dirac delta distributions remain in the
constraint equations. The skeleton Hamiltonian is exact in the test-body limit,
it leads to the Einsteinian dynamics up to the first post-Newtonian
approximation, and in the time-symmetric limit it gives the energy of the
Brill-Lindquist solution exactly. The skeleton model for binary systems may be
regarded as a kind of analytical counterpart to the numerical treatment of
orbiting Misner-Lindquist binary black holes proposed by Gourgoulhon,
Grandclement, and Bonazzola, even if they actually treat the corotating case.
Along circular orbits, the two-black-hole skeleton solution is quasi-stationary
and it fulfills the important property of equality of Komar and ADM masses.
Explicit calculations for the determination of the last stable circular orbit
of the binary system are performed up to the tenth post-Newtonian order within
the skeleton model.Comment: 15 pages, 1 figure, submitted to Phys. Rev. D, 3 references added,
minor correction
Gravitational waves from inspiralling compact binaries: Parameter estimation using second-post-Newtonian waveforms
The parameters of inspiralling compact binaries can be estimated using
matched filtering of gravitational-waveform templates against the output of
laser-interferometric gravitational-wave detectors. Using a recently calculated
formula, accurate to second post-Newtonian (2PN) order [order , where
is the orbital velocity], for the frequency sweep () induced by
gravitational radiation damping, we study the statistical errors in the
determination of such source parameters as the ``chirp mass'' , reduced
mass , and spin parameters and (related to spin-orbit and
spin-spin effects, respectively). We find that previous results using template
phasing accurate to 1.5PN order actually underestimated the errors in ,
, and . For two inspiralling neutron stars, the measurement errors
increase by less than 16 percent.Comment: 14 pages, ReVTe
Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?
We make a comparison between results from numerically generated,
quasi-equilibrium configurations of compact binary systems of black holes in
close orbits, and results from the post-Newtonian approximation. The
post-Newtonian results are accurate through third PN order (O(v/c)^6 beyond
Newtonian gravity), and include rotational and spin-orbit effects, but are
generalized to permit orbits of non-zero eccentricity. Both treatments ignore
gravitational radiation reaction. The energy E and angular momentum J of a
given configuration are compared between the two methods as a function of the
orbital angular frequency \Omega. For small \Omega, corresponding to orbital
separations a factor of two larger than that of the innermost stable orbit, we
find that, if the orbit is permitted to be slightly eccentric, with e ranging
from \approx 0.03 to \approx 0.05, and with the two objects initially located
at the orbital apocenter (maximum separation), our PN formulae give much better
fits to the numerically generated data than do any circular-orbit PN methods,
including various ``effective one-body'' resummation techniques. We speculate
that the approximations made in solving the initial value equations of general
relativity numerically may introduce a spurious eccentricity into the orbits.Comment: 6 pages, 4 figures, to be submitted to Phys. Rev.
On the Circular Orbit Approximation for Binary Compact Objects In General Relativity
One often-used approximation in the study of binary compact objects (i.e.,
black holes and neutron stars) in general relativity is the instantaneously
circular orbit assumption. This approximation has been used extensively, from
the calculation of innermost circular orbits to the construction of initial
data for numerical relativity calculations. While this assumption is
inconsistent with generic general relativistic astrophysical inspiral phenomena
where the dissipative effects of gravitational radiation cause the separation
of the compact objects to decrease in time, it is usually argued that the
timescale of this dissipation is much longer than the orbital timescale so that
the approximation of circular orbits is valid. Here, we quantitatively analyze
this approximation using a post-Newtonian approach that includes terms up to
order ({Gm/(rc^2)})^{9/2} for non-spinning particles. By calculating the
evolution of equal mass black hole / black hole binary systems starting with
circular orbit configurations and comparing them to the more astrophysically
relevant quasicircular solutions, we show that a minimum initial separation
corresponding to at least 6 (3.5) orbits before plunge is required in order to
bound the detection event loss rate in gravitational wave detectors to < 5%
(20%). In addition, we show that the detection event loss rate is > 95% for a
range of initial separations that include all modern calculations of the
innermost circular orbit (ICO).Comment: 10 pages, 12 figures, revtex
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
Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion
A particle of mass moves on a circular orbit around a nonrotating black
hole of mass . Under the assumption the gravitational waves
emitted by such a binary system can be calculated exactly numerically using
black-hole perturbation theory. If, further, the particle is slowly moving,
then the waves can be calculated approximately analytically, and expressed in
the form of a post-Newtonian expansion. We determine the accuracy of this
expansion in a quantitative way by calculating the reduction in signal-to-noise
ratio incurred when matched filtering the exact signal with a nonoptimal,
post-Newtonian filter.Comment: 5 pages, ReVTeX, 1 figure. A typographical error was discovered in
the computer code used to generate the results presented in the paper. The
corrected results are presented in an Erratum, which also incorporates new
results, obtained using the recently improved post-Newtonian calculations of
Tanaka, Tagoshi, and Sasak
Binary black hole initial data for numerical general relativity based on post-Newtonian data
With the goal of taking a step toward the construction of astrophysically
realistic initial data for numerical simulations of black holes, we for the
first time derive a family of fully general relativistic initial data based on
post-2-Newtonian expansions of the 3-metric and extrinsic curvature without
spin. It is expected that such initial data provide a direct connection with
the early inspiral phase of the binary system. We discuss a straightforward
numerical implementation, which is based on a generalized puncture method.
Furthermore, we suggest a method to address some of the inherent ambiguity in
mapping post-Newtonian data onto a solution of the general relativistic
constraints.Comment: 13 pages, 8 figures, RevTex
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