Secular evolution of orbital parameters for general bound orbits in Kerr spacetime
arXiv:2603.27941 · doi:10.1093/ptep/ptag119
Abstract
We analytically derive the secular changes of the orbital parameters, i.e., energy, angular momentum, and Carter constant, for general bound orbits in Kerr spacetime, at leading order in the mass ratio, through the 6th post-Newtonian (6PN) order and the 16th order in orbital eccentricity. We validate the formulas against high-precision numerical Teukolsky results and quantify how eccentricity affects both the achievable accuracy and the PN convergence. We then construct and test a simple ``hybrid'' approximation that combines different PN and eccentricity truncations to retain accuracy at reduced computational cost. We also assess the performance of exponential resummation at higher PN orders. These results provide building blocks for fast, (analytic) adiabatic inspiral and waveform models for extreme mass ratio inspirals relevant to space-based detectors such as the Laser Interferometer Space Antenna (LISA).
22 pages, 9 figures
References in corpus (75)
- The motion of point particles in curved spacetime
- The Effective Field Theorist's Approach to Gravitational Dynamics
- Self-force and radiation reaction in general relativity
- The TianQin project: current progress on science and technology
- Analytic black hole perturbation approach to gravitational radiation
- Concepts and status of Chinese space gravitational wave detection projects
- Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
- Setting the cornerstone for the IMRPhenomX family of models for gravitational waves from compact binaries: The dominant harmonic for non-precessing quasi-circular black holes
- Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
- Relativistic Dynamics and Extreme Mass Ratio Inspirals
- FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis
- Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
- Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis
- Gravitational waveforms for compact binaries from second-order self-force theory
- Second-order self-force calculation of the gravitational binding energy in compact binaries
- Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
- Transient resonances in the inspirals of point particles into black holes
- Gravitational self-force on generic bound geodesics in Kerr spacetime
- Gravitational-wave energy flux for compact binaries through second order in the mass ratio
- Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order
- Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime
- New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation
- The Science of the Einstein Telescope
- Computing inspirals in Kerr in the adiabatic regime. I. The scalar case
- An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
- The adiabatic evolution of orbital parameters in the Kerr spacetime
- Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole to the 11th Post-Newtonian Order
- Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach
- Comparing second-order gravitational self-force, numerical relativity and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries
- Accuracy of the Post-Newtonian Approximation: Optimal Asymptotic Expansion for Quasi-Circular, Extreme-Mass Ratio Inspirals
- Adiabatic radiation reaction to the orbits in Kerr Spacetime
- New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation II. Solutions of the Continued Fraction Equation
- Resonantly enhanced and diminished strong-field gravitational-wave fluxes
- Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals
- Gravitational Wave Astronomy With TianQin
- The Astrophysics of Resonant Orbits in the Kerr Metric
- Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
- 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
- Self-Force in the Radiation Reaction Formula -- Adiabatic Approximation of a Metric Perturbation and an Orbit --
- Gravitational radiation for extreme mass ratio inspirals to the 14th post-Newtonian order
- Calculation of radiation reaction effect on orbital parameters in Kerr spacetime
- A census of transient orbital resonances encountered during binary inspiral
- Waveform Modelling for the Laser Interferometer Space Antenna
- Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain
- Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime
- Non-local parameter degeneracy in the intrinsic space of gravitational-wave signals from extreme-mass-ratio inspirals
- "Flux-balance formulae" for extreme mass-ratio inspirals
- Eccentric-orbit EMRI gravitational wave energy fluxes to 7PN order
- Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations
- Modeling transient resonances in extreme-mass-ratio inspirals
- Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
- Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity
- Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit non-spinning extreme-mass-ratio inspirals to 19PN
- Gravitational wave surrogate model for spinning, intermediate mass ratio binaries based on perturbation theory and numerical relativity
- Impact of relativistic waveforms in LISA's science objectives with extreme-mass-ratio inspirals
- 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
- Gravitational radiation reaction
- Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals from Black-hole Perturbation Approach
- Fast inspirals and the treatment of orbital resonances
- Post-Newtonian templates for gravitational waves from compact binary inspirals
- Action-Angle formalism for extreme mass ratio inspirals in Kerr spacetime
- A one-stop function for gravitational-wave detection, identification and inference
- Non-linear effects in EMRI dynamics and their imprints on gravitational waves
- Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
- Flux-balance laws for spinning bodies under the gravitational self-force
- Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes
- Note on Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals: Retrograde Orbits
- Worldtube excision method for intermediate-mass-ratio inspirals: self-consistent evolution in a scalar-charge model
- Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole
- Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
- Building a bridge between comparable and extreme mass ratio black hole binaries: a single spin precessing model for the final state
- 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
- Constants of motion in gravitational self-force theory
- Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit