Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole to the 11th Post-Newtonian Order

Abstract

We compute the energy flux of the gravitational waves radiated by a particle of mass $\m$ in circular orbits around a rotating black hole of mass $M$ up to the 11th post-Newtonian order (11PN), i.e. $v^{22}$ beyond the leading Newtonian approximation where $v$ is the orbital velocity of the particle. By comparing the PN results for the energy flux with high precision numerical results in black hole perturbation theory, we find the region of validity in the PN approximation becomes larger with increasing PN orders. If one requires the relative error of the energy flux in the PN approximation to be less than $10^{-5}$, the energy flux at 11PN (4PN) can be used for $v⪅0.33$ ($v⪅0.13$). The region of validity can be further extended to $v⪅0.4$ if one applies a resummation method to the energy flux at 11PN. We then compare the orbital phase during two-year inspiral from the PN results with the high precision numerical results. We find that for late (early) inspirals when $q\le 0.3$ ($q\le 0.9$), where $q$ is the dimensionless spin parameter of the black hole, the difference in the phase is less than 1 ($10^{-4}$) rads and hence these inspirals may be detected in the data analysis for space detectors such as eLISA/NGO by the PN templates. We also compute the energy flux radiated into the event horizon for a particle in circular orbits around a non-rotating black hole at 22.5PN, i.e. $v^{45}$ beyond the leading Newtonian approximation, which is comparable to the PN order derived in our previous work for the energy flux to infinity at 22PN.

arXiv comment31 pages, additional datafiles are available at http://www2.yukawa.kyoto-u.ac.jp/~misao/BHPC/calcs.html

References in corpus (45)

• The motion of point particles in curved spacetime
• Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
• Analytic black hole perturbation approach to gravitational radiation
• Gravitational self force in extreme mass-ratio inspirals
• Dimensional regularization of the gravitational interaction of point masses
• The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission
• Event rate estimates for LISA extreme mass ratio capture sources
• Improved resummation of post-Newtonian multipolar waveforms from circularized compact binaries
• Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order
• Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions
• The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission: II. Inspiral trajectories and gravitational waveforms
• Celestial mechanics in Kerr spacetime
• Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections
• Post-Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries
• Comparing Effective-One-Body gravitational waveforms to accurate numerical data
• Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
• Black Hole Perturbation
• Post-Newtonian factorized multipolar waveforms for spinning, non-precessing black-hole binaries
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• Self-interaction spin effects in inspiralling compact binaries
• Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild black hole -5.5 Post-Newtonian Formula-
• Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order
• New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation
• Extreme Mass-Ratio Inspirals in the Effective-One-Body Approach: Quasi-Circular, Equatorial Orbits around a Spinning Black Hole
• Modeling Extreme Mass Ratio Inspirals within the Effective-One-Body Approach
• An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
• Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole :Effects of Black Hole Absorption
• The adiabatic evolution of orbital parameters in the Kerr spacetime
• Recoil velocity at 2PN order for spinning black hole binaries
• Next-to-leading tail-induced spin-orbit effects in the gravitational radiation flux of compact binaries
• Modeling the horizon-absorbed gravitational flux for equatorial-circular orbits in Kerr spacetime
• New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation II. Solutions of the Continued Fraction Equation
• Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol
• Spin-spin effects in radiating compact binaries
• Gravitational radiation for extreme mass ratio inspirals to the 14th post-Newtonian order
• Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime
• Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation
• Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: a numerical approach
• Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
• Second post-Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries
• Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole

Cited by in corpus (47)

• Tidal Deformation and Dissipation of Rotating Black Holes
• A multipolar effective one body waveform model for spin-aligned black hole binaries
• Remnant of binary black-hole mergers: New simulations and peak luminosity studies
• The Science of the Einstein Telescope
• A Multipolar Effective One Body Model for Non-Spinning Black Hole Binaries
• Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach
• Nonlinear-in-spin effects in effective-one-body waveform models of spin-aligned, inspiralling, neutron star binaries
• Effective one-body model for extreme-mass-ratio spinning binaries on eccentric equatorial orbits: testing radiation reaction and waveform
• Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
• Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole
• Modeling horizon absorption in spinning binary black holes using effective worldline theory
• Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
• Priorities in gravitational waveforms for future space-borne detectors: vacuum accuracy or environment?
• Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries II: the large-mass-ratio case
• Calculation of radiation reaction effect on orbital parameters in Kerr spacetime
• Improved next-to-leading order tidal heating and torquing of a Kerr black hole
• Towards a gravitational self force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals
• Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order
• iResum: a new paradigm for resumming gravitational wave amplitudes
• Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. II: the higher multipolar modes
• Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins
• The most powerful astrophysical events: Gravitational-wave peak luminosity of binary black holes as predicted by numerical relativity
• "Flux-balance formulae" for extreme mass-ratio inspirals
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Experimental mathematics meets gravitational self-force
• Post-Newtonian phase accuracy requirements for stellar black hole binaries with LISA
• Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit non-spinning extreme-mass-ratio inspirals to 19PN
• Improved gravitational radiation time-scales II: spin-orbit contributions and environmental perturbations
• The nonspinning binary black hole merger scenario revisited
• Bound orbits of a slowly evolving black hole
• Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
• Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals from Black-hole Perturbation Approach
• Post-Newtonian templates for gravitational waves from compact binary inspirals
• Gravitational memory: new results from post-Newtonian and self-force theory
• Tidal heating and torquing of the primary black hole in eccentric-orbit, non-spinning extreme-mass-ratio inspirals to 22PN order
• Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes
• Electromagnetic self-force on a charged particle on Kerr spacetime: equatorial circular orbits
• Note on Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals: Retrograde Orbits
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole
• Astrophysics with the Laser Interferometer Space Antenna
• Advancing the Effective-One-Body Framework in the Test-Mass Limit
• Post-Newtonian expansion of fluxes from a scalar charge on an inclined-spherical orbit about a Kerr black hole
• Waveform models for the gravitational-wave memory effect: Extreme mass-ratio limit and final memory offset
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits
• Secular evolution of orbital parameters for general bound orbits in Kerr spacetime