55 research outputs found

### iResum: a new paradigm for resumming gravitational wave amplitudes

We introduce a new, resummed, analytical form of the post-Newtonian (PN),
factorized, multipolar amplitude corrections $f_{\ell m}$ of the
effective-one-body (EOB) gravitational waveform of spinning, nonprecessing,
circularized, coalescing black hole binaries (BBHs). This stems from the
following two-step paradigm: (i) the factorization of the orbital
(spin-independent) terms in $f_{\ell m}$; (ii) the resummation of the residual
spin (or orbital) factors. We find that resumming the residual spin factor by
taking its inverse resummed (iResum) is an efficient way to obtain amplitudes
that are more accurate in the strong-field, fast-velocity regime. The
performance of the method is illustrated on the $\ell=2$ and $m=(1,2)$ waveform
multipoles, both for a test-mass orbiting around a Kerr black hole and for
comparable-mass BBHs. In the first case, the iResum $f_{\ell m}$'s are much
closer to the corresponding "exact" functions (obtained solving numerically the
Teukolsky equation) up to the light-ring, than the nonresummed ones, especially
when the black-hole spin is nearly extremal. The iResum paradigm is also more
efficient than including higher post-Newtonian terms (up to 20PN order): the
resummed 5PN information yields per se a rather good numerical/analytical
agreement at the last-stable-orbit, and a well-controlled behavior up to the
light-ring. For comparable mass binaries (including the highest PN-order
information available, 3.5PN), comparing EOB with Numerical Relativity (NR)
data shows that the analytical/numerical fractional disagreement at merger,
without NR-calibration of the EOB waveform, is generically reduced by iResum,
from a $40\%$ of the usual approach to just a few percents. This suggests that
EOBNR waveform models for coalescing BBHs may be improved using iResum
amplitudes.Comment: 6 pages, 7 figures. Improved discussion for the comparable-mass cas

### Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order

Using black hole perturbation theory and arbitrary-precision computer
algebra, we obtain the post-Newtonian (pN) expansions of the
linear-in-mass-ratio corrections to the spin-precession angle and tidal
invariants for a particle in circular orbit around a Schwarzschild black hole.
We extract coefficients up to 20pN order from numerical results that are
calculated with an accuracy greater than 1 part in $10^{500}$. These results
can be used to calibrate parameters in effective-one-body models of compact
binaries, specifically the spin-orbit part of the effective Hamiltonian and the
dynamically significant tidal part of the main radial potential of the
effective metric. Our calculations are performed in a radiation gauge, which is
known to be singular away from the particle. To overcome this irregularity, we
define suitable Detweiler-Whiting singular and regular fields in this gauge,
and we devise a rigorous mode-sum regularization method to compute the
invariants constructed from the regular field

### Raising and Lowering operators of spin-weighted spheroidal harmonics

In this paper we generalize the spin-raising and lowering operators of
spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted
spheroidal harmonics where $\gamma$ is an additional parameter present in the
second order ordinary differential equation governing these harmonics. One can
then generalize these operators to higher powers in $\gamma$. Constructing
these operators required calculating the $\ell$-, $s$- and $m$-raising and
lowering operators (and various combinations of them) of spin-weighted
spherical harmonics which have been calculated and shown explicitly in this
paper

### Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation

We present a novel analytic extraction of high-order post-Newtonian (pN)
parameters that govern quasi-circular binary systems. Coefficients in the pN
expansion of the energy of a binary system can be found from corresponding
coefficients in an extreme-mass-ratio inspiral (EMRI) computation of the change
$\Delta U$ in the redshift factor of a circular orbit at fixed angular
velocity. Remarkably, by computing this essentially gauge-invariant quantity to
accuracy greater than one part in $10^{225}$, and by assuming that a subset of
pN coefficients are rational numbers or products of $\pi$ and a rational, we
obtain the exact analytic coefficients. We find the previously unexpected
result that the post-Newtonian expansion of $\Delta U$ (and of the change
$\Delta\Omega$ in the angular velocity at fixed redshift factor) have
conservative terms at half-integral pN order beginning with a 5.5 pN term. This
implies the existence of a corresponding 5.5 pN term in the expansion of the
energy of a binary system.
Coefficients in the pN series that do not belong to the subset just described
are obtained to accuracy better than 1 part in $10^{265-23n}$ at $n$th pN
order. We work in a radiation gauge, finding the radiative part of the metric
perturbation from the gauge-invariant Weyl scalar $\psi_0$ via a Hertz
potential. We use mode-sum renormalization, and find high-order renormalization
coefficients by matching a series in $L=\ell+1/2$ to the large-$L$ behavior of
the expression for $\Delta U$. The non-radiative parts of the perturbed metric
associated with changes in mass and angular momentum are calculated in the
Schwarzschild gauge

### Self-force as a cosmic censor in the Kerr overspinning problem

It is known that a near-extremal Kerr black hole can be spun up beyond its
extremal limit by capturing a test particle. Here we show that overspinning is
always averted once back-reaction from the particle's own gravity is properly
taken into account. We focus on nonspinning, uncharged, massive particles
thrown in along the equatorial plane, and work in the first-order self-force
approximation (i.e., we include all relevant corrections to the particle's
acceleration through linear order in the ratio, assumed small, between the
particle's energy and the black hole's mass). Our calculation is a numerical
implementation of a recent analysis by two of us [Phys.\ Rev.\ D {\bf 91},
104024 (2015)], in which a necessary and sufficient "censorship" condition was
formulated for the capture scenario, involving certain self-force quantities
calculated on the one-parameter family of unstable circular geodesics in the
extremal limit. The self-force information accounts both for radiative losses
and for the finite-mass correction to the critical value of the impact
parameter. Here we obtain the required self-force data, and present strong
evidence to suggest that captured particles never drive the black hole beyond
its extremal limit. We show, however, that, within our first-order self-force
approximation, it is possible to reach the extremal limit with a suitable
choice of initial orbital parameters. To rule out such a possibility would
require (currently unavailable) information about higher-order self-force
corrections.Comment: 13 pages, 3 figure

### EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole

This is the first of two papers on computing the self-force in a radiation
gauge for a particle moving in circular, equatorial orbit about a Kerr black
hole. In the EMRI (extreme-mass-ratio inspiral) framework, with mode-sum
renormalization, we compute the renormalized value of the quantity
$h_{\alpha\beta}u^\alpha u^\beta$, gauge-invariant under gauge transformations
generated by a helically symmetric gauge vector; and we find the related order
$\frak{m}$ correction to the particle's angular velocity at fixed renormalized
redshift (and to its redshift at fixed angular velocity). The radiative part of
the perturbed metric is constructed from the Hertz potential which is extracted
from the Weyl scalar by an algebraic inversion\cite{sf2}. We then write the
spin-weighted spheroidal harmonics as a sum over spin-weighted spherical
harmonics and use mode-sum renormalization to find the renormalization
coefficients by matching a series in $L=\ell+1/2$ to the large-$L$ behavior of
the expression for $H := \frac12 h_{\alpha\beta}u^\alpha u^\beta$. The
non-radiative parts of the perturbed metric associated with changes in mass and
angular momentum are calculated in the Kerr gauge

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