Analytical high-order post-Newtonian expansions for spinning extreme mass ratio binaries

Abstract

We present an analytic computation of Detweiler's redshift invariant for a point mass in a circular orbit around a Kerr black hole, giving results up to 8.5 post-Newtonian order while making no assumptions on the magnitude of the spin of the black hole. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi, and employs a rigorous mode-sum regularization prescription based on the Detweiler-Whiting singular-regular decomposition. The approximations used in our approach are minimal; we use the standard self-force expansion to linear order in the mass ratio, and the standard post-Newtonian expansion in the separation of the binary. A key advantage of this approach is that it produces expressions that include contributions at all orders in the spin of the Kerr black hole. While this work applies the method to the specific case of Detweiler's redshift invariant, it can be readily extended to other gauge invariant quantities and to higher post-Newtonian orders.

Minor typos corrected, references added

References in corpus (11)

• Modeling the dynamics of tidally-interacting binary neutron stars up to merger
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• A practical, covariant puncture for second-order self-force calculations
• Nonlinear gravitational self-force. I. Field outside a small body
• Tidal invariants for compact binaries on quasi-circular orbits
• Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
• New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime

Cited by in corpus (39)

• Black holes, gravitational waves and fundamental physics: a roadmap
• Self-force and radiation reaction in general relativity
• Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach
• Evolution of small-mass-ratio binaries with a spinning secondary
• Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios
• Gravitational waves from bodies orbiting the Galactic Center black hole and their detectability by LISA
• Test black holes, scattering amplitudes and perturbations of Kerr spacetime
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
• Dissipation in extreme-mass ratio binaries with a spinning secondary
• Quasi-circular inspirals and plunges from non-spinning effective-one-body Hamiltonians with gravitational self-force information
• Second-order perturbation theory: the problem of infinite mode coupling
• New metric reconstruction scheme for gravitational self-force calculations
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• 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
• Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. III: the spinning test-body terms
• Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit non-spinning extreme-mass-ratio inspirals to 19PN
• Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
• Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime
• Horizon Surface Gravity in Corotating Black Hole Binaries
• High-order tail in Kerr spacetime
• New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: redshift invariant
• Gravitational memory: new results from post-Newtonian and self-force theory
• Elementary Integral Series for Heun Functions. With an Application to Black-Hole Perturbation Theory
• 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
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Note on Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals: Retrograde Orbits
• Connecting scattering, monodromy, and MST's renormalized angular momentum for the Teukolsky equation in Kerr spacetime
• Gravitational self-force corrections to tidal invariants for particles on eccentric orbits in a Schwarzschild spacetime
• Analytical determination of the periastron advance in spinning binaries from self-force computations
• Gravitational self-force corrections to tidal invariants for particles on circular orbits in a Kerr spacetime
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
• Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole
• Multipolar Particles in Helically Symmetric Spacetimes
• Post-Newtonian expansion of fluxes from a scalar charge on an inclined-spherical orbit about a Kerr black hole
• Redshift factor and the small mass-ratio limit in binary black hole simulations