New metric reconstruction scheme for gravitational self-force calculations

Abstract

Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a "no-string" radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of "gauge completion" as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the "gauge completion". We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order self-force calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.

arXiv comment73 pages in CQG format, 2 figures. v2 has an expanded introduction

References in corpus (49)

• The motion of point particles in curved spacetime
• Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
• Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
• Self-force and radiation reaction in general relativity
• Prospects for Fundamental Physics with LISA
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Second-order gravitational self-force
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• Gravitational self-force on generic bound geodesics in Kerr spacetime
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime
• Gravitational Self-force in a Radiation Gauge
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Black hole perturbation theory and gravitational self-force
• Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime
• Nonlinear gravitational self-force: second-order equation of motion
• 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
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• Gravitational self-force from radiation-gauge metric perturbations
• Numerical computation of second order vacuum perturbations of Kerr black holes
• A practical, covariant puncture for second-order self-force calculations
• Nonlinear gravitational self-force. I. Field outside a small body
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Self-force corrections to the periapsis advance around a spinning black hole
• Completion of metric reconstruction for a particle orbiting a Kerr black hole
• Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios
• Frequency-domain calculation of the self force: the high-frequency problem and its resolution
• Teukolsky formalism for nonlinear Kerr perturbations
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime
• On finding fields and self-force in a gauge appropriate to separable wave equations
• Analytical high-order post-Newtonian expansions for spinning extreme mass ratio binaries
• Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations
• Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
• Second-order gravitational self-force in a highly regular gauge
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• The mass and angular momentum of reconstructed metric perturbations
• On the Existence of Radiation Gauges in Petrov type II spacetimes
• Self-force: Computational Strategies
• Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime
• Time-domain metric reconstruction for hyperbolic scattering
• Time-domain metric reconstruction for self-force applications
• Electromagnetic fields on Kerr spacetime, Hertz potentials and Lorenz gauge
• New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: gyroscope precession
• Separable electromagnetic perturbations of rotating black holes
• Gauge-fixing for the completion problem of reconstructed metric perturbations of a Kerr spacetime

Cited by in corpus (7)

• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Perturbations of spinning black holes beyond General Relativity: Modified Teukolsky equation
• An approach to computing spectral shifts for black holes beyond Kerr
• Gravitational perturbations of rotating black holes in Lorenz gauge
• Slow evolution of the metric perturbation due to a quasicircular inspiral into a Schwarzschild black hole
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Flux-balance laws in scalar self-force theory