Self force on a scalar charge in Kerr spacetime: eccentric equatorial orbits

Abstract

We present a numerical code for calculating the self force on a scalar charge moving in a bound (eccentric) geodesic in the equatorial plane of a Kerr black hole. We work in the frequency domain and make use of the method of extended homogeneous solutions [Phys.\ Rev.\ D {\bf 78}, 084021 (2008)], in conjunction with mode-sum regularization. Our work is part of a program to develop a computational architecture for fast and efficient self-force calculations, alternative to time-domain methods. We find that our frequency-domain method outperforms existing time-domain schemes for small eccentricities, and, remarkably, remains competitive up to eccentricities as high as $\sim 0.7$. As an application of our code we (i) compute the conservative scalar-field self-force correction to the innermost stable circular equatorial orbit, as a function of the Kerr spin parameter; and (ii) calculate the variation in the rest mass of the scalar particle along the orbit, caused by the component of the self force tangent to the four-velocity.

26 pages, 9 figures. Minor typo corrected

References in corpus (12)

• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
• Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• Forced motion near black holes
• Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation
• Frequency-domain calculation of the self force: the high-frequency problem and its resolution
• Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole
• A Fast Frequency-Domain Algorithm for Gravitational Self-Force: I, Circular Orbits in Schwarzschild Spacetime
• Computational Efficiency of Frequency-- and Time--Domain Calculations of Extreme Mass--Ratio Binaries: Equatorial Orbits

Cited by in corpus (55)

• Black holes, gravitational waves and fundamental physics: a roadmap
• New Horizons for Fundamental Physics with LISA
• Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
• Detecting fundamental fields with LISA observations of gravitational waves from extreme mass-ratio inspirals
• Evolution of inspiral orbits around a Schwarzschild black hole
• Testing the Cosmic Censorship Conjecture with point particles: the effect of radiation reaction and the self-force
• Highly eccentric inspirals into a black hole
• 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
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• Research Update on Extreme-Mass-Ratio Inspirals
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Self-force corrections to the periapsis advance around a spinning black hole
• Self-consistent orbital evolution of a particle around a Schwarzschild black hole
• Frequency-domain algorithm for the Lorenz-gauge gravitational self-force
• Motion of charged and spinning particle influenced by dark matter field surrounding a charged dyonic black hole
• Innermost stable circular orbit of spinning particle in charged spinning black hole background
• Self-Force and Green Function in Schwarzschild spacetime via Quasinormal Modes and Branch Cut
• Eccentric self-forced inspirals into a rotating black hole
• Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals
• Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary
• Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure
• Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime
• Gravitational waves from eccentric extreme mass-ratio inspirals as probes of scalar fields
• Self-force via Green functions and worldline integration
• Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole
• New Kludge Scheme for the Construction of Approximate Waveforms for Extreme-Mass-Ratio Inspirals
• High-order expansions of the Detweiler-Whiting singular field in Kerr spacetime
• Self force on a scalar charge in Kerr spacetime: inclined circular orbits
• Generic effective source for scalar self-force calculations
• Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime
• Resonant self-force effects in extreme-mass-ratio binaries: A scalar model
• Fast spectral source integration in black hole perturbation calculations
• Importance of including small body spin effects in the modelling of intermediate mass-ratio inspirals. II Accurate parameter extraction of strong sources using higher-order spin effects
• Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits
• Self-forced inspirals with spin-orbit precession
• 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
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• Frequency-domain approach to self-force in hyperbolic scattering
• Highly eccentric EMRI waveforms via fast self-forced inspirals
• Accelerated motion and the self-force in Schwarzschild spacetime
• Accurate modeling of intermediate-mass-ratio inspirals: Exploring the form of the self-force in the intermediate-mass-ratio regime
• Scalar self-force for eccentric orbits around a Schwarzschild black hole
• Gravitational self-force in non-vacuum spacetimes: an effective field theory derivation
• Scalar field self-force effects on a particle orbiting a Reissner-Nordstrom black hole
• Self force on an accelerated particle
• Self-force on an arbitrarily coupled scalar charge in cylindrical thin-shell spacetimes
• Post-Newtonian expansion of fluxes from a scalar charge on an inclined-spherical orbit about a Kerr black hole
• Scalar Self-force for High Spin Black Holes
• Regularization of a scalar charged particle for generic orbits in Kerr spacetime
• Self force from equivalent periodic sources
• Extreme mass-ratio inspirals as probes of scalar fields: eccentric equatorial orbits around Kerr black holes
• Hyperboloidal method for frequency-domain self-force calculations