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.

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

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Cited by in corpus (10)

• Complete waveform model for compact binaries on eccentric orbits
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Evolution of small-mass-ratio binaries with a spinning secondary
• Tidal invariants for compact binaries on quasi-circular orbits
• Self-Force Calculations with a Spinning Secondary
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Self force on a scalar charge in Kerr spacetime: inclined circular orbits
• Modified Gravity Corrections in Fundamental Orbital Frequencies in Kerr Spacetime