111 research outputs found
Fast Self-forced Inspirals
We present a new, fast method for computing the inspiral trajectory and
gravitational waves from extreme mass-ratio inspirals that can incorporate all
known (and future) self-force results. Using near-identity (averaging)
transformations we formulate equations of motion that do not explicitly depend
upon the orbital phases of the inspiral, making them fast to evaluate, and
whose solutions track the evolving constants of motion, orbital phases and
waveform phase of a full self-force inspiral to , where is the
(small) mass ratio. As a concrete example, we implement these equations for
inspirals of non-spinning (Schwarzschild) binaries. Our code computes inspiral
trajectories in milliseconds which is a speed up of 2-5 orders of magnitude
(depending on the mass-ratio) over previous self-force inspiral models which
take minutes to hours to evaluate. Computing two-year duration waveforms using
our new model we find a mismatch better than with respect to
waveforms computed using the (slower) full self-force models. The speed of our
new approach is comparable with kludge models but has the added benefit of
easily incorporating self-force results which will, once known, allow the
waveform phase to be tracked to sub-radian accuracy over an inspiral.Comment: 33 pages, code available at http://bhptoolkit.org
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
Highly eccentric inspirals into a black hole
We model the inspiral of a compact stellar-mass object into a massive
nonrotating black hole including all dissipative and conservative
first-order-in-the-mass-ratio effects on the orbital motion. The techniques we
develop allow inspirals with initial eccentricities as high as and
initial separations as large as to be evolved through many thousands
of orbits up to the onset of the plunge into the black hole. The inspiral is
computed using an osculating elements scheme driven by a hybridized self-force
model, which combines Lorenz-gauge self-force results with highly accurate flux
data from a Regge-Wheeler-Zerilli code. The high accuracy of our hybrid
self-force model allows the orbital phase of the inspirals to be tracked to
within radians or better. The difference between self-force models
and inspirals computed in the radiative approximation is quantified.Comment: Updated to reflect published versio
Evolution of small-mass-ratio binaries with a spinning secondary
We calculate the evolution and gravitational-wave emission of a spinning
compact object inspiraling into a substantially more massive (non-rotating)
black hole. We extend our previous model for a non-spinning binary [Phys. Rev.
D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force.
For spin-aligned binaries we calculate the dephasing of the inspiral and
associated waveforms relative to models that do not include spin-curvature
effects. We find this dephasing can be either positive or negative depending on
the initial separation of the binary. For binaries in which the spin and
orbital angular momentum are not parallel, the orbital plane precesses and we
use a more general osculating element prescription to compute inspirals.Comment: 17 pages, 6 figure
Particle on the Innermost Stable Circular Orbit of a Rapidly Spinning Black Hole
We compute the radiation emitted by a particle on the innermost stable
circular orbit of a rapidly spinning black hole both (a) analytically, working
to leading order in the deviation from extremality and (b) numerically, with a
new high-precision Teukolsky code. We find excellent agreement between the two
methods. We confirm previous estimates of the overall scaling of the power
radiated, but show that there are also small oscillations all the way to
extremality. Furthermore, we reveal an intricate mode-by-mode structure in the
flux to infinity, with only certain modes having the dominant scaling. The
scaling of each mode is controlled by its conformal weight, a quantity that
arises naturally in the representation theory of the enhanced near-horizon
symmetry group. We find relationships to previous work on particles orbiting in
precisely extreme Kerr, including detailed agreement of quantities computed
here with conformal field theory calculations performed in the context of the
Kerr/CFT correspondence.Comment: 15 pages, 4 figures, v2: reference added, minor changes, matches
published versio
Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
Extreme mass-ratio inspirals (EMRIs) are expected to have considerable
eccentricity when emitting gravitational waves (GWs) in the LISA band.
Developing GW templates that remain phase accurate over these long inspirals
requires the use of second-order self-force theory and practical second-order
self-force calculations are now emerging for quasi-circular EMRIs. These
calculations rely on effective-source regularization techniques in the
frequency domain that presently are specialized to circular orbits. Here we
make a first step towards more generic second-order calculations by extending
the frequency domain effective-source approach to eccentric orbits. In order to
overcome the slow convergence of the Fourier sum over radial modes, we develop
a new extended effective-sources approach which builds upon the method of
extended particular solutions. To demonstrate our new computational technique
we apply it a toy scalar-field problem which is conceptually similar to the
gravitational case.Comment: 23 pages, 16 figures; updated to reflect published versio
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