Self-force via a Green's function decomposition

Abstract

The gravitational field of a particle of small mass μmoving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(μ). One part is an inhomogeneous field which, near the particle, looks like the μ/r field distorted by the local Riemann tensor; it does not depend on the behavior of the source in either the infinite past or future. The other part is a homogeneous field and includes the ``tail term''; it completely determines the self force effects of the particle interacting with its own gravitational field, including radiation reaction. Self force effects for scalar, electromagnetic and gravitational fields are all described in this manner.

PRD, in press. Enhanced emphasis on the equivalence principle

Cited by in corpus (255)

• Black holes, gravitational waves and fundamental physics: a roadmap
• The motion of point particles in curved spacetime
• Self-force and radiation reaction in general relativity
• Perturbative Approach to an orbital evolution around a Supermassive black hole
• Gravitational self force in extreme mass-ratio inspirals
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile
• A Rigorous Derivation of Gravitational Self-force
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Second-order gravitational self-force
• Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
• Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
• Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
• Gravitational self-force on generic bound geodesics in Kerr spacetime
• Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole
• The self-consistent gravitational self-force
• Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
• Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results
• Second Order Gravitational Self-Force
• Post-Newtonian and Numerical Calculations of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Self-force of a scalar field for circular orbits about a Schwarzschild black hole
• Gravitational Self-force in a Radiation Gauge
• The Science of the Einstein Telescope
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Highly eccentric inspirals into a black hole
• Computing inspirals in Kerr in the adiabatic regime. I. The scalar case
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• Black hole perturbation theory and gravitational self-force
• EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole
• Nonlinear gravitational self-force: second-order equation of motion
• Perspective on gravitational self-force analyses
• Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
• Analytical high-order post-Newtonian expansions for extreme mass ratio binaries
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• The adiabatic evolution of orbital parameters in the Kerr spacetime
• Gravitational self-torque and spin precession in compact binaries
• Gravitational self-force on a particle orbiting a Kerr black hole
• Low multipole contributions to the gravitational self-force
• Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime
• Research Update on Extreme-Mass-Ratio Inspirals
• Self-force as a cosmic censor
• Generation and propagation of nonlinear quasi-normal modes of a Schwarzschild black hole
• Mechanics of extended masses in general relativity
• A practical, covariant puncture for second-order self-force calculations
• Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation
• Nonlinear gravitational self-force. I. Field outside a small body
• Gravitational radiation reaction and second order perturbation theory
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Self force on a scalar charge in Kerr spacetime: circular equatorial orbits
• Tidal invariants for compact binaries on quasi-circular orbits
• Overcharging higher-dimensional black holes with point particles
• Self force on a scalar charge in Kerr spacetime: eccentric equatorial orbits
• Self-Force Calculations with a Spinning Secondary
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Limitations of the adiabatic approximation to the gravitational self-force
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
• Scalar field self-force effects on orbits about a Schwarzschild black hole
• Self-consistent orbital evolution of a particle around a Schwarzschild black hole
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• Hamilton-Jacobi equation for spinning particles near black holes
• Motion of small objects in curved spacetimes: An introduction to gravitational self-force
• High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime
• Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Second-order gravitational self-force
• Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
• On finding fields and self-force in a gauge appropriate to separable wave equations
• Gauge Problem in the Gravitational Self-Force I. Harmonic Gauge Approach in the Schwarzschild Background
• Frequency-domain algorithm for the Lorenz-gauge gravitational self-force
• Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations
• A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole
• Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
• Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
• Bobbing and Kicks in Electromagnetism and Gravity
• A Fast Frequency-Domain Algorithm for Gravitational Self-Force: I, Circular Orbits in Schwarzschild Spacetime
• Motion in classical field theories and the foundations of the self-force problem
• Self-Force and Green Function in Schwarzschild spacetime via Quasinormal Modes and Branch Cut
• Eccentric self-forced inspirals into a rotating black hole
• Perturbative evolution of particle orbits around Kerr black holes: time domain calculation
• Second-order perturbation theory: the problem of infinite mode coupling
• Second-order gravitational self-force in a highly regular gauge
• Self-force with (3+1) codes: a primer for numerical relativists
• An Efficient Pseudospectral Method for the Computation of the Self-force on a Charged Particle: Circular Geodesics around a Schwarzschild Black Hole
• Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Construction of the second-order gravitational perturbations produced by a compact object
• Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime
• "Flux-balance formulae" for extreme mass-ratio inspirals
• Pseudospectral Collocation Methods for the Computation of the Self-Force on a Charged Particle: Generic Orbits around a Schwarzschild Black Hole
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order
• Singular perturbation techniques in the gravitational self-force problem
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• From the self-force problem to the Radiation reaction formula
• Self-force via Green functions and worldline integration
• Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries
• Experimental mathematics meets gravitational self-force
• Gravitational self-force in the ultra-relativistic limit: The 'large-N' expansion
• General Relativistic Dynamics of an Extreme Mass-Ratio Binary interacting with an External Body
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Applying the effective-source approach to frequency-domain self-force calculations
• Self-Force with a Stochastic Component from Radiation Reaction of a Scalar Charge Moving in Curved Spacetime
• Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
• Transition from inspiral to plunge for eccentric equatorial Kerr orbits
• High-order expansions of the Detweiler-Whiting singular field in Kerr spacetime
• Gauge and motion in perturbation theory
• Self-forces from generalized Killing fields
• Numerical computation of the EOB potential q using self-force results
• Orbital evolution of a particle around a black hole: II. Comparison of contributions of spin-orbit coupling and the self force
• Self force via m-mode regularization and 2+1D evolution: Foundations and a scalar-field implementation on Schwarzschild
• Metric perturbations from eccentric orbits on a Schwarzschild black hole: I. Odd-parity Regge-Wheeler to Lorenz gauge transformation and two new methods to circumvent the Gibbs phenomenon
• Gauge Problem in the Gravitational Self-Force II. First Post Newtonian Force under Regge-Wheeler Gauge
• Self force on a scalar charge in Kerr spacetime: inclined circular orbits
• Effective source approach to self-force calculations
• Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime
• Generic effective source for scalar self-force calculations
• Resonant self-force effects in extreme-mass-ratio binaries: A scalar model
• 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
• Electromagnetic self-forces and generalized Killing fields
• High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries
• Self-forces on extended bodies in electrodynamics
• Evolution of the Carter constant for a resonant inspiral into a Kerr black hole: I. The scalar case
• Gauge and Averaging in Gravitational Self-force
• Quasi-local contribution to the gravitational self-force
• Radiation Reaction in Schwarzschild Spacetime: Retarded Green's Function via Hadamard-WKB Expansion
• From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect
• The force on a point charge source of the classical electromagnetic field
• Regularization of static self-forces
• Self-force Regularization in the Schwarzschild Spacetime
• Self-force correction to geodetic spin precession in Kerr spacetime
• Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime
• Self-force as probe of internal structure
• Effective stress-energy tensors, self-force, and broken symmetry
• Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
• Self-force from reconstructed metric perturbations: numerical implementation in Schwarzschild spacetime
• Ultralight scalars and resonances in black-hole physics
• Whirling orbits around twirling black holes from conformal symmetry
• Static Kerr Green's Function in Closed Form and an Analytic Derivation of the Self-Force for a Static Scalar Charge in Kerr Space-Time
• Improvement on the metric reconstruction scheme in the Regge-Wheeler-Zerilli formalism
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Excitation of Kerr quasinormal modes in extreme--mass-ratio inspirals
• Gravitational self-force in nonvacuum spacetimes
• Gravitational backreaction on a cosmic string: Formalism
• An action for reaction in general dimension
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source
• Frequency-domain approach to self-force in hyperbolic scattering
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Particle motion under the conservative piece of the self-force is Hamiltonian
• Accelerated motion and the self-force in Schwarzschild spacetime
• Self-forces on static bodies in arbitrary dimensions
• Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?
• Quantum Radiation Reaction and the Green's Function Decomposition
• Testing gravity with Extreme-Mass-Ratio Inspirals
• Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling
• Gravitational Self-Force Regularization in the Regge-Wheeler and Easy Gauges
• Massive-Field Approach to the Scalar Self Force in Curved Spacetime
• Equations of Motion in General Relativity of a Small Charged Black Hole
• Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations
• Simulations of Extreme-Mass-Ratio Inspirals Using Pseudospectral Methods
• Flux-balance laws for spinning bodies under the gravitational self-force
• Foundations of the self-force problem in arbitrary dimensions
• Modulation of the gravitational waveform by the effect of radiation reaction
• Self-forces in arbitrary dimensions
• Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes
• Scalar self-force for eccentric orbits around a Schwarzschild black hole
• Inspirals into a charged black hole
• A fully relativistic radial fall
• Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge
• A new method to integrate (2+1)-wave equations with Dirac's delta functions as sources
• Post-Newtonian expansion of the spin-precession invariant for eccentric-orbit non-spinning extreme-mass-ratio inspirals to 9PN and $e^{16}$
• Regularization of the second-order gravitational perturbations produced by a compact object
• Self force of a static electric charge near a Schwarzschild Star
• High-order post-Newtonian expansion of the redshift invariant for eccentric-orbit non-spinning extreme-mass-ratio inspirals
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Gravitational Waves from binary black holes in the extreme mass ratio regime: Self-force calculations
• Multi-domain spectral method for self-force calculations
• Combined gravitational and electromagnetic self-force on charged particles in electrovac spacetimes
• Motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws
• Electromagnetic self-force on a charged particle on Kerr spacetime: equatorial circular orbits
• Scalar self-force on a static particle in Schwarzschild using the massive field approach
• Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin
• Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions
• Probing global aspects of a geometry by the self-force on a charge: Spherical thin-shell wormholes
• Gravitational self-force in non-vacuum spacetimes: an effective field theory derivation
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Gravitational self-force corrections to tidal invariants for particles on eccentric orbits in a Schwarzschild spacetime
• Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial
• Static Self-Forces in a Five-Dimensional Black Hole Spacetime
• Gravitational self-force corrections to tidal invariants for spinning particles on circular orbits in a Schwarzschild spacetime
• High-Accuracy Comparison between the Post-Newtonian and Self-Force Dynamics of Black-Hole Binaries
• Radiation reaction in 2+1 electrodynamics
• A source-free integration method for black hole perturbations and self-force computation: Radial fall
• Motion of small bodies in general relativity: foundations and implementations of the self-force
• Gravitational self-force corrections to tidal invariants for particles on circular orbits in a Kerr spacetime
• Self-forced evolutions of an implicit rotating source: A natural framework to model comparable and intermediate mass-ratio systems from inspiral through ringdown
• Worldtube excision method for intermediate-mass-ratio inspirals: self-consistent evolution in a scalar-charge model
• Radiation reaction and energy-momentum conservation
• Scalar field self-force effects on a particle orbiting a Reissner-Nordstrom black hole
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
• Self force on an accelerated particle
• Indirect (source-free) integration method. II. Self-force consistent radial fall
• Analytic Approximations in GR and Gravitational Waves
• Toward Second-Order Self-Force for Eccentric Extreme-Mass Ratio Inspirals in Schwarzschild Spacetime
• Simple, efficient method of calculating the Detweiler-Whiting singular field to very high order
• Aspects of electrostatics in BTZ geometries
• Self-force on a scalar charge in a circular orbit about a Reissner-Nordström black hole
• The first law of binary black hole scattering
• Self-force as a probe of global structure
• Self force in 2+1 electrodynamics
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Self-force on an arbitrarily coupled scalar charge in cylindrical thin-shell spacetimes
• Free fall and self-force: an historical perspective
• Particle-without-Particle: a practical pseudospectral collocation method for linear partial differential equations with distributional sources
• Self-action in Gravity
• Self-force of a scalar charge in the space-time of extreme charged anti-dilatonic wormhole
• Analytic approximations, perturbation methods, and their applications
• Self-force on an arbitrarily coupled static scalar particle in a wormhole space-time
• Excited by a quantum field: Does shape matter?
• Spin-2 Green's Functions on Kerr in Radiation Gauge
• Radiation reaction in curved even-dimensional spacetime
• Scalar Self-force for High Spin Black Holes
• Regularization of a scalar charged particle for generic orbits in Kerr spacetime
• Relieving scale disparity in binary black hole simulations
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• Arbitrarily coupled massive scalar field in conical thin-shell spacetimes
• Comments on initial conditions for the Abraham-Lorentz(-Dirac) equation
• Constants of motion in gravitational self-force theory
• Flux-balance laws in scalar self-force theory
• Perturbative correction terms to electromagnetic self-force due to metric perturbation : astrophysical and cosmological implications
• Spacetime Symmetries and Kepler's Third Law
• Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
• The singular field used to calculate the self-force on non-spinning and spinning particles
• Harmonic gauge perturbations of the Schwarzschild metric
• Eternal binaries
• The Radial Action from Probe Amplitudes to All Orders
• High-order comparisons between post-Newtonian and perturbative self forces
• Self-force via energy-momentum and angular momentum balance equations
• Self-force and the Schwarzschild star
• Redshift factor and the small mass-ratio limit in binary black hole simulations
• Hyperboloidal method for frequency-domain self-force calculations
• Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime
• Causal Poisson bracket via deformation quantization
• Adiabatic evolution due to the conservative scalar self-force during orbital resonances
• Constructing the self-force
• Multipole decomposition of the gravitational field of a point mass at the black hole horizon
• Self force from equivalent periodic sources