Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation

Abstract

We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a sample of results for mildly eccentric orbits as well as ``zoom-whirl'' orbits.

18 pages, 18 figures, RevTeX4 some typos fixed, published version

References in corpus (10)

• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• Self-force via a Green's function decomposition
• Mode sum regularization approach for the self-force in black hole spacetime
• Axiomatic approach to radiation reaction of scalar point particles in curved spacetime
• Self-force of a scalar field for circular orbits about a Schwarzschild black hole
• Understanding initial data for black hole collisions
• Scalar field self-force effects on orbits about a Schwarzschild black hole
• Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
• A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit

Cited by in corpus (52)

• Black holes, gravitational waves and fundamental physics: a roadmap
• The motion of point particles in curved spacetime
• Gravitational self force in extreme mass-ratio inspirals
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• Zoom-Whirl Orbits in Black Hole Binaries
• The self-consistent gravitational self-force
• Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
• Research Update on Extreme-Mass-Ratio Inspirals
• Self-force as a cosmic censor
• Self force on a scalar charge in Kerr spacetime: circular equatorial orbits
• Eccentric black hole mergers and zoom-whirl behavior from elliptic inspirals to hyperbolic encounters
• Self force on a scalar charge in Kerr spacetime: eccentric equatorial orbits
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Frequency-domain calculation of the self force: the high-frequency problem and its resolution
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
• Self-consistent orbital evolution of a particle around a Schwarzschild black hole
• 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
• Frequency-domain algorithm for the Lorenz-gauge gravitational self-force
• Second-order perturbation theory: problems on large scales
• A Fast Frequency-Domain Algorithm for Gravitational Self-Force: I, Circular Orbits in Schwarzschild Spacetime
• Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure
• An Efficient Pseudospectral Method for the Computation of the Self-force on a Charged Particle: Circular Geodesics around a Schwarzschild Black Hole
• Self-force with (3+1) codes: a primer for numerical relativists
• Pseudospectral Collocation Methods for the Computation of the Self-Force on a Charged Particle: Generic Orbits around a Schwarzschild Black Hole
• Self-force via Green functions and worldline integration
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• High-order expansions of the Detweiler-Whiting singular field in Kerr spacetime
• Self force via m-mode regularization and 2+1D evolution: Foundations and a scalar-field implementation on Schwarzschild
• Induced Spins from Scattering Experiments of Initially Nonspinning Black Holes
• Self force on a scalar charge in Kerr spacetime: inclined circular orbits
• Effective source approach to self-force calculations
• Quasi-local contribution to the scalar self-force: Geodesic Motion
• Generic effective source for scalar self-force calculations
• Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime
• Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits
• Time-domain metric reconstruction for hyperbolic scattering
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• Frequency-domain approach to self-force in hyperbolic scattering
• Adaptive Mesh Refinement for Characteristic Grids
• Scalar self-force for eccentric orbits around a Schwarzschild black hole
• Modulation of the gravitational waveform by the effect of radiation reaction
• 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
• Scalar field self-force effects on a particle orbiting a Reissner-Nordstrom black hole
• Hidden Momentum and Black Hole Kicks
• Regularization of a scalar charged particle for generic orbits in Kerr spacetime
• Discontinuous collocation methods and gravitational self-force applications
• Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs
• Fourth order indirect integration method for black hole perturbations: even modes