Analytical solutions of bound timelike geodesic orbits in Kerr spacetime

Abstract

We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $\lambda$ as the independent variable. Mino time decouples the radial and polar motion of a particle and hence leads to forms more useful to estimate three fundamental frequencies, radial, polar and azimuthal motion, for the bound timelike geodesics in Kerr spacetime. This paper gives the first derivation of the analytical expressions of the fundamental frequencies. This paper also gives the first derivation of the analytical expressions of all coordinates for the bound timelike geodesics using Mino time. These analytical expressions should be useful not only to investigate physical properties of Kerr geodesics but more importantly to applications related to the estimation of gravitational waves from the extreme mass ratio inspirals.

A typo in the first expression in equation 21 was fixed

References in corpus (7)

• Gravitational wave snapshots of generic extreme mass ratio inspirals
• A Periodic Table for Black Hole Orbits
• Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
• Periapsis and gravitomagnetic precessions of stellar orbits in Kerr and Kerr-de Sitter black hole spacetimes
• An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
• Dynamics of Black Hole Pairs I: Periodic Tables
• Circular and non-circular nearly horizon-skimming orbits in Kerr spacetimes

Cited by in corpus (150)

• FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis
• Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times
• Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
• The Null Geodesics of the Kerr Exterior
• Gravitational self-force on generic bound geodesics in Kerr spacetime
• Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times
• Spherical orbits around a Kerr black hole
• The Science of the Einstein Telescope
• Highly eccentric inspirals into a black hole
• Black hole perturbation theory and gravitational self-force
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• The location of the last stable orbit in Kerr spacetime
• Charged particle motion in Kerr-Newmann space-times
• Forced motion near black holes
• Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach
• Evolution of small-mass-ratio binaries with a spinning secondary
• Timelike geodesics in Naked Singularity and Black Hole Spacetimes
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Importance of transient resonances in extreme-mass-ratio inspirals
• Growth of resonances and chaos for a spinning test particle in the Schwarzschild background
• Periodic orbits around a spherically symmetric naked singularity
• Hamilton-Jacobi equation for spinning particles near black holes
• Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime
• The role of the supermassive black hole spin in the estimation of the EMRI event rate
• Resonantly enhanced and diminished strong-field gravitational-wave fluxes
• Exciting black hole modes via misaligned coalescences: I. Inspiral, transition, and plunge trajectories using a generalized Ori-Thorne procedure
• Particle motion near high-spin black holes
• Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
• Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals
• Strong gravity Lense-Thirring Precession in Kerr and Kerr-Taub-NUT spacetimes
• Test particle motion in the space-time of a Kerr black hole pierced by a cosmic string
• Assessing the impact of transient orbital resonances
• The Astrophysics of Resonant Orbits in the Kerr Metric
• Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
• Gyroscopes orbiting black holes: A frequency-domain approach to precession and spin-curvature coupling for spinning bodies on generic Kerr orbits
• Spinning test body orbiting around a Kerr black hole: Eccentric equatorial orbits and their asymptotic gravitational-wave fluxes
• Calculation of radiation reaction effect on orbital parameters in Kerr spacetime
• Astrophysically relevant bound trajectories around a Kerr black hole
• Eccentric self-forced inspirals into a rotating black hole
• A census of transient orbital resonances encountered during binary inspiral
• Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain
• Periodic orbits around Kerr Sen black holes
• Isofrequency pairing of geodesic orbits in Kerr geometry
• Resonantly enhanced kicks from equatorial small mass-ratio inspirals
• Analytic treatment of geodesics in five-dimensional Myers-Perry space--times
• "Flux-balance formulae" for extreme mass-ratio inspirals
• Importance of tidal resonances in extreme-mass-ratio inspirals
• Analytic Kludge Waveforms for Extreme Mass Ratio Inspirals of Charged Object around Kerr-Newman Black Hole
• Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations
• New Kludge Scheme for the Construction of Approximate Waveforms for Extreme-Mass-Ratio Inspirals
• Modeling transient resonances in extreme-mass-ratio inspirals
• Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
• Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
• Perihelion Precession and Shadows near Blackholes and Naked Singularities
• Towards an observational test of black hole versus naked singularity at the galactic center
• Numerical computation of the EOB potential q using self-force results
• Boundary to bound dictionary for generic Kerr orbits
• Observables for bound orbital motion in axially symmetric space-times
• Analytic solutions for the motion of spinning particles near spherically symmetric black holes and exotic compact objects
• Resonant self-force effects in extreme-mass-ratio binaries: A scalar model
• Fundamental frequencies and resonances from eccentric and precessing binary black hole inspirals
• Kerr Geodesics in Terms of Weierstrass Elliptic Functions
• Fast spectral source integration in black hole perturbation calculations
• Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits
• Phase space mixing in the equatorial plane of a Kerr black hole
• Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
• Lense-Thirring Precession in Plebański-Demiański spacetimes
• Self-forced inspirals with spin-orbit precession
• An analytic toy model for relativistic accretion in Kerr spacetime
• Extreme mass ratio inspirals into black holes surrounded by matter
• A complete characterisation of the orbital shapes of the non-circular Kerr geodesic solutions with circular orbit constants of motion
• Self-force correction to geodetic spin precession in Kerr spacetime
• Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals from Black-hole Perturbation Approach
• Relativistic aerodynamics of spinning black holes
• Periodic orbits and gravitational waveforms in quantum-corrected black hole spacetimes
• Ultralight scalars and resonances in black-hole physics
• Fast inspirals and the treatment of orbital resonances
• Strong-field tidal distortions of rotating black holes: II. Horizon dynamics from eccentric and inclined orbits
• Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
• Near-horizon geodesics of high-spin black holes
• Simulation of geodesic trajectory of charged BTZ black holes in massive gravity
• Generalized gravitomagnetic clock effect
• Dynamics of spinning particles in Reissner-Nordström black hole exterior
• A Newtonian analogue of Kerr black hole
• Gyroscope precession along general timelike geodesics in a Kerr black hole spacetime
• Probing fundamental physics with Extreme Mass Ratio Inspirals: a full Bayesian inference for scalar charge
• Action-Angle formalism for extreme mass ratio inspirals in Kerr spacetime
• Relativistic propagation and frame dragging time delay in the timing of a pulsar orbiting the supermassive black hole SgrA*
• Investigation the geodesic motion of three dimensional rotating black holes
• A Note on Celestial Mechanics in Kerr Spacetime
• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
• Charged test-particle scattering and effective one-body metrics with spin
• A geometric origin for quasi-periodic oscillations in black hole X-ray binaries
• The equatorial motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime
• Black hole photon ring beyond General Relativity: an integrable parametrization
• Relativistic model of binary extreme-mass-ratio inspiral systems and their gravitational radiation
• Geodesic Motions near an improved Schwarzschild black hole
• Peaking into the abyss: Characterizing the merger of equatorial-eccentric-geodesic plunges in rotating black holes
• Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory
• Approach to the separatrix with eccentric orbits
• Gravitational waves for eccentric extreme mass ratio inspirals of self-dual spacetime
• Photon Boomerang in a Nearly Extreme Kerr Metric
• Observables of a test-mass along an inclined orbit in a post-Newtonian approximated Kerr spacetime to leading-order-quadratic-in-spin
• Geodesic motion in the five-dimensional Myers-Perry-AdS spacetime
• Electrogeodesics in the di-hole Majumdar-Papapetrou spacetime
• Gravitational wave fluxes on generic orbits in near-extreme Kerr spacetime: higher spin and large eccentricity
• Particle motion in the field of a five-dimensional charged black hole
• Eccentricity distribution of extreme mass ratio inspirals
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
• Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole
• Stability of circular geodesics in equatorial plane of Kerr spacetime
• Timelike orbits around accelerating black holes
• Dynamics of test particles in the five-dimensional, charged, rotating EMCS spacetime
• Cumulative effect of orbital resonances in extreme-mass-ratio inspirals
• Dynamical Measurement of Supermassive Black Hole Masses: QPE Timing Method
• Retrograde Precession of Relativistic Orbits and the Quest for Charged Black Holes
• Motion of charged particles around a scalarized black hole in Kaluza-Klein theory
• Spherical inspirals of spinning bodies into Kerr black holes
• Geodesic motion around a supersymmetric AdS5 black hole
• Post-Minkowskian solution for the small-deflection motion of test particles in Kerr-Newman spacetime
• Post-Newtonian expansion of fluxes from a scalar charge on an inclined-spherical orbit about a Kerr black hole
• Resonant interactions from dynamical perturbers on generic orbits around an extreme mass ratio inspiral
• Impact of mass transfer on the orbital evolution of a white dwarf close to an intermediate-mass black hole
• MALBEC: a new CUDA-C ray-tracer in General Relativity
• A note on the conversion of orbital angles for extreme mass ratio inspirals
• Captured are circularized: A relativistic treatment of extreme mass ratio inspirals crossing accretion disks
• Spherical particle orbits around a rotating black hole in massive gravity
• Observable signature of magnetic tidal coupling in hierarchical triple systems
• Constants of motion in gravitational self-force theory
• KerrGeoPy: A Python Package for Computing Timelike Geodesics in Kerr Spacetime
• An Analytic, Fully Relativistic Framework for Tidal Disruption Event Streams in Schwarzschild Geometry
• Classification of radial Kerr geodesic motion
• Periodic Orbits and Gravitational Wave Radiation of Black Hole in EGB gravity
• Secular evolution of orbital parameters for general bound orbits in Kerr spacetime
• Massive particle surfaces and black hole shadows from intrinsic curvature
• Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
• Off-equatorial deflections and gravitational lensing. II. In general stationary and axisymmetric spacetimes
• Geodesic equations and algebro-geometric methods
• Modified Gravity Corrections in Fundamental Orbital Frequencies in Kerr Spacetime
• Nonuniform Particle Injection into Black Hole Jets by Radiative Magnetic Reconnection
• Equatorial periodic orbits and gravitational wave signatures in Euler-Heisenberg black holes surrounded by perfect fluid dark matter
• Revisiting critical orbits of test particles traveling in a black hole background
• Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits
• Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits
• Extreme mass-ratio inspirals as probes of scalar fields: eccentric equatorial orbits around Kerr black holes
• All analytic solutions for geodesic motion in axially symmetric space-times
• Prospects for detecting asteroid-mass primordial black holes in extreme mass-ratio inspirals with continuous gravitational waves
• Gravitational Wave Signatures of Quasi-Periodic Eruptions: LISA Detection Prospects for RX J1301.9+2747
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane