Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians

Abstract

The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short-range behavior of the integrands around the sources. The Hamiltonian of a test-spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post-Newtonian approximate) Poincaré algebra are applied. Along the way a self-contained overview for the computation of the 3PN ADM point-mass Hamiltonian is provided, too.

56 pages, minor corrections to match published version

References in corpus (32)

• Tests of general relativity from timing the double pulsar
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• An improved analytical description of inspiralling and coalescing black-hole binaries
• 3+1 Formalism and Bases of Numerical Relativity
• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Tidal effects in binary neutron star coalescence
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes
• Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries
• Effective field theory calculation of second post-Newtonian binary dynamics
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• ADM canonical formalism for gravitating spinning objects
• Spin effects on gravitational waves from inspiraling compact binaries at second post-Newtonian order
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Foundations of multiple black hole evolutions
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Canonical Formulation of Spin in General Relativity
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• Close encounters of three black holes
• Numerical evolution of multiple black holes with accurate initial data
• Three-body equations of motion in successive post-Newtonian approximations
• The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory
• Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries
• Accurate and efficient gravitational waveforms for certain galactic compact binaries
• Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction

Cited by in corpus (45)

• Black holes, gravitational waves and fundamental physics: a roadmap
• The Effective Field Theorist's Approach to Gravitational Dynamics
• A catalog of 174 binary black-hole simulations for gravitational-wave astronomy
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• A new effective-one-body description of coalescing nonprecessing spinning black-hole binaries
• Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order
• Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Gravitational self-torque and spin precession in compact binaries
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme
• Exploring New Physics Frontiers Through Numerical Relativity
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• Parameter Estimation of Gravitational Waves from Precessing BH-NS Inspirals with higher harmonics
• How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
• Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Post-Newtonian Quasicircular Initial Orbits for Numerical Relativity
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order
• Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework
• Fourth post-Newtonian effective-one-body Hamiltonians with generic spins
• Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: I. Non-Locality in Time and Infra-Red Divergencies
• Probing evolution of binaries influenced by the spin-orbit resonances
• The propagation delay in the timing of a pulsar orbiting a supermassive black hole
• Analytic approximations, perturbation theory, effective field theory methods and their applications
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Time-domain inspiral templates for spinning compact binaries in quasi-circular orbits described by their orbital angular momenta
• Quantum point particle approximation of spinning black holes and compact stars