Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions

Abstract

Continuing our analytic computation of the first-order self-force contribution to Detweiler's redshift variable we provide the exact expressions of the ninth and ninth-and-a-half post-Newtonian terms.

arXiv comment4 pages, revtex 4.1 macros used

References in corpus (14)

• Effective one-body approach to general relativistic two-body dynamics
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• The complete non-spinning effective-one-body metric at linear order in the mass ratio
• Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
• Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion
• Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results
• 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
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

Cited by in corpus (32)

• Black holes, gravitational waves and fundamental physics: a roadmap
• Self-force and radiation reaction in general relativity
• Fourth post-Newtonian effective one-body dynamics
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Analytical high-order post-Newtonian expansions for extreme mass ratio binaries
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• First Law of Mechanics for Compact Binaries on Eccentric Orbits
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole
• Quasi-circular inspirals and plunges from non-spinning effective-one-body Hamiltonians with gravitational self-force information
• Logarithmic tail contributions to the energy function of circular compact binaries
• On the four-loop static contribution to the gravitational interaction potential of two point masses
• Towards a gravitational self force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals
• New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• 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
• Experimental mathematics meets gravitational self-force
• Spin-dependent two-body interactions from gravitational self-force computations
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails
• High post-Newtonian order gravitational self-force analytical results for eccentric orbits around a Kerr black hole
• Conservative second-order gravitational self-force on circular orbits and the effective one-body formalism
• Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime
• Self-force correction to geodetic spin precession in Kerr spacetime
• New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: redshift invariant
• Detweiler's redshift invariant for spinning particles along circular orbits on a Schwarzschild background
• Electromagnetic self-force on a charged particle on Kerr spacetime: equatorial circular orbits
• Tidal invariants along the world line of an extended body in the Kerr spacetime
• Gravitational self-force corrections to tidal invariants for spinning particles on circular orbits in a Schwarzschild spacetime