28 research outputs found
Frequency-domain algorithm for the Lorenz-gauge gravitational self-force
State-of-the-art computations of the gravitational self-force (GSF) on
massive particles in black hole spacetimes involve numerical evolution of the
metric perturbation equations in the time-domain, which is computationally very
costly. We present here a new strategy, based on a frequency-domain treatment
of the perturbation equations, which offers considerable computational saving.
The essential ingredients of our method are (i) a Fourier-harmonic
decomposition of the Lorenz-gauge metric perturbation equations and a numerical
solution of the resulting coupled set of ordinary equations with suitable
boundary conditions; (ii) a generalized version of the method of extended
homogeneous solutions [Phys. Rev. D {\bf 78}, 084021 (2008)] used to circumvent
the Gibbs phenomenon that would otherwise hamper the convergence of the Fourier
mode-sum at the particle's location; and (iii) standard mode-sum
regularization, which finally yields the physical GSF as a sum over regularized
modal contributions. We present a working code that implements this strategy to
calculate the Lorenz-gauge GSF along eccentric geodesic orbits around a
Schwarzschild black hole. The code is far more efficient than existing
time-domain methods; the gain in computation speed (at a given precision) is
about an order of magnitude at an eccentricity of 0.2, and up to three orders
of magnitude for circular or nearly circular orbits. This increased efficiency
was crucial in enabling the recently reported calculation of the long-term
orbital evolution of an extreme mass ratio inspiral [Phys. Rev. D {\bf 85},
061501(R) (2012)]. Here we provide full technical details of our method to
complement the above report.Comment: 27 pages, 4 figure
Numerical computation of the EOB potential q using self-force results
The effective-one-body theory (EOB) describes the conservative dynamics of
compact binary systems in terms of an effective Hamiltonian approach. The
Hamiltonian for moderately eccentric motion of two non-spinning compact objects
in the extreme mass-ratio limit is given in terms of three potentials: . By generalizing the first law of mechanics for
(non-spinning) black hole binaries to eccentric orbits, [\prd{\bf92}, 084021
(2015)] recently obtained new expressions for and in terms
of quantities that can be readily computed using the gravitational self-force
approach. Using these expressions we present a new computation of the EOB
potential by combining results from two independent numerical self-force
codes. We determine for inverse binary separations in the range . Our computation thus provides the first-ever strong-field
results for . We also obtain in our entire domain to a
fractional accuracy of . We find to our results are compatible
with the known post-Newtonian expansions for and in the
weak field, and agree with previous (less accurate) numerical results for
in the strong field.Comment: 4 figures, numerical data at the end. Fixed the typos, added the
journal referenc
Critical phenomena at the threshold of immediate merger in binary black hole systems: the extreme mass ratio case
In numerical simulations of black hole binaries, Pretorius and Khurana
[Class. Quant. Grav. {\bf 24}, S83 (2007)] have observed critical behaviour at
the threshold between scattering and immediate merger. The number of orbits
scales as along any one-parameter family of initial
data such that the threshold is at . Hence they conjecture that in
ultrarelavistic collisions almost all the kinetic energy can be converted into
gravitational waves if the impact parameter is fine-tuned to the threshold. As
a toy model for the binary, they consider the geodesic motion of a test
particle in a Kerr black hole spacetime, where the unstable circular geodesics
play the role of critical solutions, and calculate the critical exponent
. Here, we incorporate radiation reaction into this model using the
self-force approximation. The critical solution now evolves adiabatically along
a sequence of unstable circular geodesic orbits under the effect of the
self-force. We confirm that almost all the initial energy and angular momentum
are radiated on the critical solution. Our calculation suggests that, even for
infinite initial energy, this happens over a finite number of orbits given by
, where is the (small) mass ratio. We derive
expressions for the time spent on the critical solution, number of orbits and
radiated energy as functions of the initial energy and impact parameter.Comment: Version published in PR
A Fast Frequency-Domain Algorithm for Gravitational Self-Force: I, Circular Orbits in Schwarzschild Spacetime
Fast, reliable orbital evolutions of compact objects around massive black
holes will be needed as input for gravitational wave search algorithms in the
data stream generated by the planned Laser Interferometer Space Antenna (LISA).
Currently, the state of the art is a time-domain code by [Phys. Rev. D{\bf 81},
084021, (2010)] that computes the gravitational self-force on a point-particle
in an eccentric orbit around a Schwarzschild black hole. Currently, time-domain
codes take up to a few days to compute just one point in parameter space. In a
series of articles, we advocate the use of a frequency-domain approach to the
problem of gravitational self-force (GSF) with the ultimate goal of orbital
evolution in mind. Here, we compute the GSF for a particle in a circular orbit
in Schwarzschild spacetime. We solve the linearized Einstein equations for the
metric perturbation in Lorenz gauge. Our frequency-domain code reproduces the
time-domain results for the GSF up to times faster for small
orbital radii. In forthcoming companion papers, we will generalize our
frequency-domain methods to include bound (eccentric) orbits in Schwarzschild
and (eventually) Kerr spacetimes for computing the GSF, where we will employ
the method of extended homogeneous solutions [Phys. Rev. D {\bf 78}, 084021
(2008)].Comment: 26 pages, 4 figures, with minor typos now fixe
A hybrid post-Newtonian -- effective-one-body scheme for spin-precessing compact-binary waveforms
We introduce \texttt{TEOBResumSP}: an efficient, accurate hybrid scheme for
generating gravitational waveforms from spin-precessing compact binaries. The
precessing waveforms are generated via the established technique of Euler
rotating the non-precessing \texttt{TEOBResumS} waveforms from a precessing
frame to an inertial frame. We obtain the Euler angles by solving the
post-Newtonian precession equations expanded to second post-Newtonian order.
Current version of \texttt{TEOBResumSP} produces precessing waveforms through
the inspiral phase up to the onset of the merger. We compare
\texttt{TEOBResumSP} to current state-of-the-art precessing approximants
\texttt{NRSur7dq4}, \texttt{SEOBNRv4PHM}, and \texttt{IMRPhenomPv3HM} for 200
cases of precessing compact binary inspirals with orbital inclinations up to 90
degrees, mass ratios up to four, and the effective precession parameter
up to 0.75. We further provide an extended comparison with
\texttt{SEOBNRv4PHM} involving 1030 more inspirals with and mass
ratios up to 10. We find that 91\% of the
\texttt{TEOBResumSP}-\texttt{NRSur7dq4} matches, 85\% of the
\texttt{TEOBResumSP}-\texttt{SEOBNRv4PHM} matches, and 77\% of the
\texttt{TEOBResumSP}-\texttt{IMRPhenomPv3HM} matches are greater than .
Most disagreements occur for large mass ratios and . We
identify the mismatch of the \emph{non}-precessing mode as one of the
leading causes of disagreements. We also introduce a new parameter,
, to measure the strength of precession and hint that
the mismatch between the above approximants shows an exponential dependence on
though this requires further study. Our results
indicate that \texttt{TEOBResumSP} is on its way to becoming a robust
precessing approximant to be employed in the parameter estimation of
generic-spin compact binaries.Comment: 23 pages, 14 figures. Matches the accepted Phys. Rev. D version
modulo abridged abstract, American vs. British English, and some figure
placement
Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
The gravitational self-force (GSF) and post-Newtonian (PN) schemes are
complementary approximation methods for modelling the dynamics of compact
binary systems. Comparison of their results in an overlapping domain of
validity provides a crucial test for both methods, and can be used to enhance
their accuracy, e.g. via the determination of previously unknown PN parameters.
Here, for the first time, we extend such comparisons to noncircular
orbits---specifically, to a system of two nonspinning objects in a bound
(eccentric) orbit. To enable the comparison we use a certain orbital-averaged
quantity that generalizes Detweiler's redshift invariant.
The functional relationship , where
and are the frequencies of the radial and azimuthal
motions, is an invariant characteristic of the conservative dynamics. We
compute numerically through linear
order in the mass ratio , using a GSF code which is based on a
frequency-domain treatment of the linearized Einstein equations in the Lorenz
gauge. We also derive analytically
through 3PN order, for an arbitrary , using the known near-zone 3PN metric
and the generalized quasi-Keplerian representation of the motion. We
demonstrate that the piece of the analytical PN prediction is
perfectly consistent with the numerical GSF results, and we use the latter to
estimate yet unknown pieces of the 4PN expression at .Comment: 44 pages, 2 figures, 4 table