# Analytical high-order post-Newtonian expansions for extreme mass ratio binaries

@article{Kavanagh2015AnalyticalHP,
title={Analytical high-order post-Newtonian expansions for extreme mass ratio binaries},
author={Chris Kavanagh and A. Ottewill and Barry Wardell},
journal={Physical Review D},
year={2015},
volume={92},
pages={084025}
}
• Published 8 March 2015
• Physics
• Physical Review D
We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling…
58 Citations

## Tables from this paper

Analytical high-order post-Newtonian expansions for spinning extreme mass ratio binaries
• Physics
• 2016
We present an analytic computation of Detweiler's redshift invariant for a point mass in a circular orbit around a Kerr black hole, giving results up to 8.5 post-Newtonian order while making no
Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit nonspinning extreme-mass-ratio inspirals to the 19th order
We develop new high-order results for the post-Newtonian (PN) expansions of the energy and angular momentum fluxes at infinity for eccentric-orbit extreme-mass-ratio inspirals (EMRIs) on a
High-order comparisons between post-Newtonian and perturbative self forces
• Physics
• 2015
Recent numerical and analytic computations based on the self-force (SF) formalism in general relativity showed that half-integral post-Newtonian (PN) terms, i.e. terms involving odd powers of 1/c,
Tidal Effects in the Post-Minkowskian Expansion.
• Physics
Physical review letters
• 2020
The leading and, for the first time, next-to-leading order post-Minkowskian finite size corrections to the conservative Hamiltonian, together with their associated scattering amplitudes and scattering angles are computed.
High post-Newtonian order gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole
• Physics
• 2016
We present the first analytic computation of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in {\it eccentric} orbit around a {\it spinning} black hole. Our results give
Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Physics
• 2015
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
Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN order for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
• Physics
• 2020
We present an extension of work in an earlier paper showing high precision comparisons between black hole perturbation theory and post-Newtonian (PN) theory in their region of overlapping validity
Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole
• Physics
• 2016
We analytically compute, through the six-and-a-half post-Newtonian order, the second-order-in-eccentricity piece of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in
Note on accuracy of the post-Newtonian approximation for extreme-mass ratio inspirals: retrograde orbits
• Physics, Geology
• 2017
The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of
Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• Physics, Geology
• 2017
In this work we present an analytical gravitational self-force calculation of the spin-orbit precession along an eccentric orbit around a Schwarzschild black hole, following closely the recent

## References

SHOWING 1-10 OF 14 REFERENCES
High-order tail in Schwarzschild spacetime
• Physics
• 2015
We present an analysis of the behaviour at late-times of linear field perturbations of a Schwarzschild black hole space-time. In particular, we give explicit analytic expressions for the field
Octupolar invariants for compact binaries on quasicircular orbits
• Physics
• 2015
We extend the gravitational self-force methodology to identify and compute new $O(\mu)$ tidal invariants for a compact body of mass $\mu$ on a quasi-circular orbit about a black hole of mass \$M \gg
“A and B”:
Direct fabrication of large micropatterned single crystals. p1205 21 Feb 2003. (news): Academy plucks best biophysicists from a sea of mediocrity. p994 14 Feb 2003.
and E
• Takasugi, Prog.Theor.Phys. 96, 549
• 1996
(b)
and T
• Damour,
• 2014
and N
• Sago, Phys.Rev. D82, 084036
• 2010
Electronic archive of post-newtonian coefficients
High - order tail in schwarzschild space - time , ” ( 2015 ) , in preparation . [ 24 ] S . L . Detweiler
• Phys . Rev . D Living Rev . Rel .