Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole

Abstract

For a self-gravitating particle of mass μin orbit around a Kerr black hole of mass M >> μ, we compute the O(μ/M) shift in the frequency of the innermost stable circular equatorial orbit (ISCEO) due to the conservative piece of the gravitational self-force acting on the particle. Our treatment is based on a Hamiltonian formulation of the dynamics in terms of geodesic motion in a certain locally-defined effective smooth spacetime. We recover the same result using the so-called first law of binary black-hole mechanics. We give numerical results for the ISCEO frequency shift as a function of the black hole's spin amplitude, and compare with predictions based on the post-Newtonian approximation and the effective one-body model. Our results provide an accurate strong-field benchmark for spin effects in the general relativistic two-body problem.

arXiv comment5 pages, 1 table, 1 figure, matches version published in PRL. Raw data of H_int/mu are available at http://link.aps.org/supplemental/10.1103/PhysRevLett.113.161101

References in corpus (47)

• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• Detector configuration of KAGRA - the Japanese cryogenic gravitational-wave detector
• Transition from inspiral to plunge in binary black hole coalescences
• The motion of point particles in curved spacetime
• Gravitational Radiation Reaction to a Particle Motion
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Effective-one-body model for black-hole binaries with generic mass ratios and spins
• Self-force via a Green's function decomposition
• The distribution and cosmic evolution of massive black hole spins
• Perturbative Approach to an orbital evolution around a Supermassive black hole
• Gravitational self force in extreme mass-ratio inspirals
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• An improved effective-one-body Hamiltonian for spinning black-hole binaries
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• Mode sum regularization approach for the self-force in black hole spacetime
• The Transition from Inspiral to Plunge for a Compact Body in a Circular Equatorial Orbit Around a Massive, Spinning Black Hole
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• The Spin of Supermassive Black Holes
• Remnant Masses, Spins and Recoils from the Merger of Generic Black-Hole Binaries
• Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
• On the mass radiated by coalescing black-hole binaries
• Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• The self-consistent gravitational self-force
• Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results
• Thermodynamics of binary black holes and neutron stars
• Innermost circular orbit of binary black holes at the third post-Newtonian approximation
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole
• Intermediate-mass-ratio black hole binaries: intertwining numerical and perturbative techniques
• Mechanics of extended masses in general relativity
• Periastron advance in spinning black hole binaries: comparing effective-one-body and Numerical Relativity
• Self force on a scalar charge in Kerr spacetime: eccentric equatorial orbits
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• First Law of Mechanics for Black Hole Binaries with Spins
• Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force
• Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime
• High-order expansions of the Detweiler-Whiting singular field in Kerr spacetime
• Aligned Spins: Orbital Elements, Decaying Orbits, and Last Stable Circular Orbit to high post-Newtonian Orders
• A Note on Celestial Mechanics in Kerr Spacetime

Cited by in corpus (69)

• Black holes, gravitational waves and fundamental physics: a roadmap
• Self-force and radiation reaction in general relativity
• Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes
• Overspinning a Kerr black hole: the effect of self-force
• The Science of the Einstein Telescope
• Highly eccentric inspirals into a black hole
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• Research Update on Extreme-Mass-Ratio Inspirals
• 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
• Evolution of small-mass-ratio binaries with a spinning secondary
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Self-force corrections to the periapsis advance around a spinning black hole
• Tidal invariants for compact binaries on quasi-circular orbits
• First Law of Mechanics for Compact Binaries on Eccentric Orbits
• Importance of transient resonances in extreme-mass-ratio inspirals
• Second-order perturbation theory: problems on large scales
• Motion of charged and spinning particle influenced by dark matter field surrounding a charged dyonic black hole
• Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
• Innermost stable circular orbit of spinning particle in charged spinning black hole background
• Dissipation in extreme-mass ratio binaries with a spinning secondary
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• Gyroscopes orbiting black holes: A frequency-domain approach to precession and spin-curvature coupling for spinning bodies on generic Kerr orbits
• Eccentric self-forced inspirals into a rotating black hole
• "Flux-balance formulae" for extreme mass-ratio inspirals
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• Circular orbit of a test particle and phase transition of a black hole
• Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails
• Innermost stable circular orbits of charged spinning test particles
• General Relativistic Dynamics of an Extreme Mass-Ratio Binary interacting with an External Body
• Transition from Inspiral to Plunge: A Complete Near-Extremal Trajectory and Associated Waveform
• Redshift factor and the first law of binary black hole mechanics in numerical simulations
• Self force on a scalar charge in Kerr spacetime: inclined circular orbits
• Fundamental frequencies and resonances from eccentric and precessing binary black hole inspirals
• Tidal deformations of a binary system induced by an external Kerr black hole
• Octupolar invariants for compact binaries on quasi-circular orbits
• Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits
• Self-force: Computational Strategies
• Conservative second-order gravitational self-force on circular orbits and the effective one-body formalism
• Slow evolution of the metric perturbation due to a quasicircular inspiral into a Schwarzschild black hole
• Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
• Minimum energy and the end of the inspiral in the post-Newtonian approximation
• Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Constraint on Brans-Dicke theory from intermediate/extreme mass ratio inspirals
• Gravitational self-force in nonvacuum spacetimes
• Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system
• Accelerated motion and the self-force in Schwarzschild spacetime
• Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?
• Geometrized effective-one-body formalism for extreme-mass-ratio limits: Generic orbits
• On the integrability of extended test body dynamics around black holes
• Electromagnetic self-force on a charged particle on Kerr spacetime: equatorial circular orbits
• Gravitational self-force corrections to tidal invariants for particles on eccentric orbits in a Schwarzschild spacetime
• Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes
• Scalar field self-force effects on a particle orbiting a Reissner-Nordstrom black hole
• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• First Law of Mechanics for Spinning Compact Binaries: Dipolar Order
• Stable circular orbits of spinning test particles around accelerating Kerr black hole
• The first law of binary black hole scattering
• Regularization of a scalar charged particle for generic orbits in Kerr spacetime
• Extended bodies with spin induced quadrupoles on circular equatorial orbits in Kerr spacetime
• Scalar Self-force for High Spin Black Holes
• Self-force and fluid resonances
• Constants of motion in gravitational self-force theory
• Eternal binaries
• Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits
• Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole