Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions

Abstract

We present a new technique for time-domain numerical evolution of the scalar field generated by a pointlike scalar charge orbiting a black hole. Time-domain evolution offers an efficient way for calculating black hole perturbations, especially as input for computations of the local self force acting on orbiting particles. In Kerr geometry, the field equations are not fully separable in the time domain, and one has to tackle them in 2+1 dimensions (two spatial dimensions and time; the azimuthal dependence is still separable). A technical difficulty arises when the source of the field is a pointlike particle, as the 2+1-dimensional perturbation is then singular: Each of the azimuthal modes diverges logarithmically at the particle. To deal with this problem we split the numerical domain into two regions: Inside a thin worldtube surrounding the particle's worldline we solve for a regularized variable, obtained from the full field by subtracting out a suitable ``puncture'' function, given analytically. Outside this worldtube we solve for the full, original field. The value of the evolution variable is adjusted across the boundary of the worldtube. In this work we demonstrate the applicability of this method in the example of circular orbits around a Schwarzschild black hole (refraining from exploiting the spherical symmetry of the background, and working in 2+1 dimensions).

Accepted for publication in PRD, minor typographical corrections, references updated, 25 pages, 22 eps figures

References in corpus (26)

• LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy
• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• A simple construction of initial data for multiple black holes
• Self-force via a Green's function decomposition
• Mode sum regularization approach for the self-force in black hole spacetime
• Calculating the gravitational self force in Schwarzschild spacetime
• Dynamics of perturbations of rotating black holes
• Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
• Axiomatic approach to radiation reaction of scalar point particles in curved spacetime
• Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
• Dynamics of Scalar Fields in the Background of Rotating Black Holes
• Computing the gravitational self-force on a compact object plunging into a Schwarzschild black hole
• Gravitational self-force on a particle orbiting a Kerr black hole
• Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases
• Regularization parameters for the self force in Schwarzschild spacetime: I. scalar case
• Radiation-reaction force on a particle plunging into a black hole
• Numerical integration of the Teukolsky Equation in the time domain
• On finding fields and self-force in a gauge appropriate to separable wave equations
• A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole
• Covariant Self-force Regularization of a Particle Orbiting a Schwarzschild Black Hole - Mode Decomposition Regularization -
• Perturbative evolution of particle orbits around Kerr black holes: time domain calculation
• Accurate time-domain gravitational waveforms for extreme-mass-ratio binaries
• A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole
• Teukolsky evolution of particle orbits around Kerr black holes in the time domain: elliptic and inclined orbits
• A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems

Cited by in corpus (62)

• 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
• 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
• Second Order Gravitational Self-Force
• Nonlinear gravitational self-force: second-order equation of motion
• Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
• Research Update on Extreme-Mass-Ratio Inspirals
• A practical, covariant puncture for second-order self-force calculations
• Nonlinear gravitational self-force. I. Field outside a small body
• 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
• Self-consistent orbital evolution of a particle around a Schwarzschild black hole
• 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
• 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
• Second-order perturbation theory: problems on large scales
• A comprehensive model of soft interactions in the LHC era
• Self-Force and Green Function in Schwarzschild spacetime via Quasinormal Modes and Branch Cut
• 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
• Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime
• Pseudospectral Collocation Methods for the Computation of the Self-Force on a Charged Particle: Generic Orbits around a Schwarzschild Black Hole
• The Eccentric Behavior of Inspiraling Compact Binaries
• Self-force via Green functions and worldline integration
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• New Kludge Scheme for the Construction of Approximate Waveforms for Extreme-Mass-Ratio Inspirals
• Applying the effective-source approach to frequency-domain self-force calculations
• Quasinormal modes and Regge poles of the canonical acoustic hole
• Gauge and motion in perturbation theory
• 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
• Effective source approach to self-force calculations
• Quasi-local contribution to the scalar self-force: Geodesic Motion
• Fast spectral source integration in black hole perturbation calculations
• Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime
• Generic effective source for scalar self-force calculations
• Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits
• Constraint on Brans-Dicke theory from intermediate/extreme mass ratio inspirals
• 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
• Gravitational backreaction on a cosmic string: Formalism
• Excitation of Kerr quasinormal modes in extreme--mass-ratio inspirals
• Accelerated motion and the self-force in Schwarzschild spacetime
• Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations
• Scalar self-force for eccentric orbits around a Schwarzschild black hole
• A new method to integrate (2+1)-wave equations with Dirac's delta functions as sources
• Second-order gravitational self-force in a highly regular gauge: Covariant and coordinate punctures
• Motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws
• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Toward Second-Order Self-Force for Eccentric Extreme-Mass Ratio Inspirals in Schwarzschild Spacetime
• Regularization of a scalar charged particle for generic orbits in Kerr spacetime
• Eternal binaries
• Exceeding the conformal limit inside rotating neutron stars: Implications to modified theories of gravity
• Confronting eikonal and post-Kerr methods with numerical evolution of scalar field perturbations in spacetimes beyond Kerr
• Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime
• Summary of GR18 Numerical Relativity parallel sessions (B1/B2 and B2), Sydney, 8-13 July 2007
• Hyperboloidal method for frequency-domain self-force calculations