A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime

Abstract

A compact object moving on a quasicircular orbit about a Schwarzschild black hole gradually spirals inward due to the dissipative action of its gravitational self-force. But in addition to driving the inspiral, the self-force has a conservative piece. Within a second-order self-force formalism, I derive a second-order generalization of Detweiler's redshift variable, which provides a gauge-invariant measure of conservative effects on quasicircular orbits. I sketch a frequency-domain numerical scheme for calculating this quantity. Once this scheme has been implemented, its results may be used to determine high-order terms in post-Newtonian theory and parameters in effective-one-body theory.

arXiv comment20 pages, 1 figure, version to appear in PRD, additional references, minor typos corrected

References in corpus (56)

• Effective one-body approach to general relativistic two-body dynamics
• The motion of point particles in curved spacetime
• Gravitational Radiation Reaction to a Particle Motion
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Self-force via a Green's function decomposition
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• Gravitational self force in extreme mass-ratio inspirals
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• 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
• Binary black holes in circular orbits. II. Numerical methods and first results
• Periastron Advance in Black-Hole Binaries
• Second-order gravitational self-force
• Binary black holes in circular orbits. I. A global spacetime approach
• Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
• Evolution of inspiral orbits 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 Correction to the Binding Energy of Compact Binary Systems
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole
• Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
• The self-consistent gravitational self-force
• Gravitational self force and gauge transformations
• Testing the Cosmic Censorship Conjecture with point particles: the effect of radiation reaction and the self-force
• Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
• Thermodynamics of binary black holes and neutron stars
• 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
• High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations
• EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole
• Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
• Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
• 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
• Nonlinear gravitational self-force. I. Field outside a small body
• Gravitational radiation reaction and second order perturbation theory
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• Periastron Advance in Spinning Black Hole Binaries: Gravitational Self-Force from Numerical Relativity
• Limitations of the adiabatic approximation to the gravitational self-force
• Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force
• Second-order gravitational self-force
• On the Geroch-Traschen class of metrics
• Construction of the second-order gravitational perturbations produced by a compact object
• Periodic Solutions of the Einstein Equations for Binary Systems
• Applying the effective-source approach to frequency-domain self-force calculations
• Generic effective source for scalar self-force calculations
• Quasi-stationary binary inspiral II: Radiation-balanced boundary conditions
• The Periodic Standing-Wave Approximation: Overview and Three Dimensional Scalar Models
• The periodic standing-wave approximation: post-Minkowski computation
• The periodic standing-wave approximation: computations in full general relativity

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